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Higher Derivations and a Theorem By Herstein
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Miguel Ferrero Claus HaetingerIn this paper we extend to the higher derivations a well-known result proved by Herstein concerning derivations in prime rings. We prove results which imply that every Jordan higher derivation of a 2-torsion-free semiprime ring is a higher derivation. -
Maximal Ideals in Near-Rings And Semigroups
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: HenryE. Heatherly RalphP. TucciThis paper gives conditions that guarantee that a near-ring or a semi- group has maximal right, left, or two-sided ideals. Stronger results are obtained for those semigroups which are adjoint semigroups of rings. Examples are given which illustrate and delimit... -
On *-Essential Ideals and Biideals of Rings with Involution
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: D.I.C. MendesLet R be a ring with involution *. We describe the structure of R, when R has no proper *-essential *-ideals (*-biideals) and also when R has a *-essential minimal *-biideal. -
A Pointfree Study of Bases For Spaces Of Minimal Prime Ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Melvin Henriksen Joanne Walters-WaylandLet C (X) denote the ring of all real-valued continuous functions on a topological space X, and mX its space of minimal prime ideals with the hull-kernel topology. It has a base consisting of clopen sets and which contains the... -
Derivations on ρ-banach Algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Amir KhosraviLet A be a ρ-Banach algebra with radical R and let D be a derivation on A. We generalize Johnson's theorem, Sinclair's theorem and Thomas's theorem (Singer-Wermer's conjecture) to ρ-Banach algebras. If K = {x ∈ R: for every n... -
Maximal Ideals in Rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: HenryE. Heatherly RalphP. TucciThis paper gives necessary and sufficient conditions which guarantee that a ring have maximal left, right, or two-sided ideals. The relations of rings without maximal ideals to the Jacobson and Brown-McCoy radical are discussed. Examples of rings without maximal ideals... -
On rings generating supernilpotent and special atoms
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: H. France-Jackson N.J. GroenewaldWe study prime rings which generate supernilpotent (respectively special) atoms, that is, atoms of the lattice of all supernilpotent (respectively special) radicals. A prime ring A is called a **-ring if the smallest special class containing A is closed under... -
(Φ, M)–extensions of near-rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mark FaragIn this paper, we define and study a generalization of matrix, polynomial, and group near-rings. New results on ideal essentiality and lying over are obtained. -
Representation of slim algebraic regular cozero maps
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. Karimi FeizabadiIn this paper a new tool, the cozero maps, is introduced to study algebraic structures in pointfree topology, which generalizes cozero elements and the cozero part of a frame. The slim regular algebraic cozero maps are represented. We proved that... -
On the maximal ideal space of extended analytic lipschitz algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: TaherG. Honary Sirous MoradiLet X be a compact, plane set and let K be a compact subset of X. We introduce new classes of Lipschitz algebras Lip(X, K, α), lip(X, K, α), consisting of those continuous functions f on X such that f|K... -
Ideals in Heyting Semilattices and Open Homomorphisms
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jorge Picado Aleš Pultr Anna TozziSubfitness and its relation to openness and completeness is studied in the context of Heyting semilattices. A formally weaker condition (c-subfitness) is shown to be necessary and sufficient for openness and completeness to coincide. For a large class of spatial... -
A Few Points on Pointfree Pseudocompactness
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Themba Dube Phethiwe MatutuWe present several characterizations of completely regular pseudocompact frames. The first is an extension to frames of characterizations of completely regular pseudocompact spaces given by Väänänen. We follow with an embedding-type characterization stating that a completely regular frame is pseudocompact... -
Semigroups of transformations with fixed sets
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Preeyanuch Honyam --- Department of Mathematics, Faculty of Science, Thailand Jintana Sanwong --- Department of Mathematics, Faculty of Science, ThailandLet T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X,... -
Long-standing open problems of Banach space theory: My personal top ten
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Albrecht Pietsch* --- , GermanyEvery serious scientist wants to discover fundamental results. However, due to outer circumstances expressed by the slogan ‘publish or perish,’ the reality looks quite different: too many mathematicians are led to deal only with problems that promise a quick and... -
A note on non-monogenity of number fields arised from sextic trinomials
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Anuj Jakhar --- Indian Institute of Technology (IIT), India Sumandeep Kaur --- Panjab University, IndiaLet K = Q (θ) be an algebraic number field with θ a root of an irreducible polynomial f(x) = x 6 + axm + b belonging to ℤ[x] and 1 ≤ m ≤ 5. Let OK be the... -
Adult weight measurement: decoding the terminology used in literature
Item type: Journal Article • Journal: South African Journal of Clinical Nutrition • Authors: Christen Renée Lahner --- Department of Human Nutrition and Dietetics, South AfricaThere are various types of names given to describe the adult weight measurement. The most commonly used terms (actual body weight, estimated body weight, ideal body weight and adjusted body weight) have been defined and summarized to assist in their... -
Practicing psychologists’ understanding of the athletic-body ideal internalisation: Implications for classification and treatment
Item type: Journal Article • Journal: Journal of Psychology in Africa • Authors: Lindi Williams --- , South Africa Del Naidoo --- , South Africa Ruan Spies --- , South AfricaThis study explored how practicing psychologists make sense of the athletic-body ideal when internalised by their clients. Utilising a grounded theory approach, we interviewed a purposive sample of nine psychologists to explore their understanding of the athletic-body ideal, with a... -
Characterizations of maximal z°-ideals of C(X) and real maximal ideals of q(X)
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Z. Arjmandnezhad --- Shahid Chamran University of ahvaz, Iran F. Azarpanah --- Shahid Chamran University of ahvaz, Iran A.A. Hesari --- Shahid Chamran University of ahvaz, Iran A.R. Salehi --- Petroleum University of Technology, IranIn this paper we first give elementwise characterizations of real maximal ideals and maximal z°-ideals of C(X). Next, using this we characterize the real maximal ideals of the classical ring of quotients q(X) of C(X) and also maximal z°-ideals of... -
On rings related to filial and left filial rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: D.I.C. Mendes --- University of Beira Interior, PortugalA ring R is called filial (left weakly filial) if it satisfies the following condition: for all subrings J and I of R, if J is an ideal of I and I is an ideal of R, then J is... -
On S-1-absorbing prime and weakly S-1-absorbing prime ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Najib Mahdou --- University S.M. Ben Abdellah Fez, Morocco Abdeslam Mimouni --- King Fahd University of Petroleum & Minerals, Saudi Arabia Youssef Zahir --- Mohammed-V University in Rabat, MoroccoLet A be a commutative ring with identity and S be a multiplicative subset of A. In this paper, we introduce and study the notions of S-1-absorbing and weakly S-1-absorbing prime ideals as generalizations of the notion of prime ideals... -
Summability of sequences and extensions of operator ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jan H. Fourie --- North-West University, South Africa Elroy D. Zeekoei --- North-West University, South AfricaGiven a Banach space Y, the so-called right Y and left Y-extensions of operator ideals are introduced and applied to the study of operator ideal properties of well-known classes of operators on Banach spaces. The key is to introduce a... -
Boundedness of the Hilbert transform in Lorentz spaces and applications to operator ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: K.S. Tulenov --- Al-Farabi Kazakh National University, KazakhstanIn this paper, it is investigated the optimal range of the classical Hilbert transform in Lorentz spaces of functions and its non-commutative counterparts including a triangular truncation operator in Schatten-Lorentz ideals. Some applications of obtained results to operator Lipschitz functions... -
Representation theorems for closed ideals of CB (X)
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Alireza Olfati --- Yasouj University, IranLet CB (X) be the Banach algebra of all continuous bounded ℂ-valued functions on a completely regular Hausdorff space X equipped with the supremum norm. We provide representation theorems for arbitrary closed ideals of CB (X). Indeed, for a closed... -
Some further remarks on characterized subgroups generated by modular simple density
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Ayan Ghosh --- Jadavpur University, IndiaIn this short note we have constructed an uncountable tower of characterized subgroups using the notion of modular simple density [8] which subsequently gives the solution of Problem 2.15 [7] in a more general setting. -
Inverses and order boundedness of invertible ideal operators
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Kazım Özcan --- , Turkey Bahri Turan --- Gazi University, TurkeyIn this paper, we investigate that under which conditions the inverse of an invertible ideal operator becomes an ideal operator. To determine conditions, in the first case, we consider the center of a Riesz space and achieve the solution by... -
Connectedness modulo an ideal; a characterization theorem
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: M.R. Koushesh --- Isfahan University of Technology, IranLet X be a topological space and let be an ideal of subsets of X. The space X is called connected modulo if there is no continuous mapping f : X → [0, 1] which is 2-valued modulo in the... -
On common index divisor and monogenity of certain number fields defined by trinomials X 6 + AX + B
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Lhoussain El Fadil --- Sidi mohamed ben Abdellah University, MoroccoFor a number field K defined by a trinomial F (x) = x 6 + ax + b ∈ ℤ[x], Jakhar and Kumar gave some necessary conditions on a and b, which guarantee the non-monogenity of K [25]. In this... -
On dual-classical Krull dimension of rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Sayed Malek Javdannezhad --- Shahid Rajaee Teacher Training University, Iran Sayedeh Fatemeh Mousavinasab --- Shahid Chamran University of Ahvaz, Iran Nasrin Shirali --- Shahid Chamran University of Ahvaz, IranAn ideal L of a ring R is said to be strongly hollow (briefly, sh-ideal) if L ⊆ A + B implies that either L ⊆ A or L ⊆ B, for every pair A and B of ideals of... -
The complexity of a numerical semigroup
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: J.I. García-García --- Universidad de Cádiz, Spain M.A. Moreno-Frías --- Universidad de Cádiz, Spain J.C. Rosales --- Universidad de Granada, Spain A. Vigneron-Tenorio --- Universidad de Cádiz, SpainLet S and Δ be numerical semigroups. A numerical semigroup S is an I(Δ)-semigroup if S \ {0} is an ideal of Δ. We denote by S is an I(Δ)-semigroup}, and we say that Δ is an ideal extension... -
On the index divisors and monogenity of number fields defined by x 5 + ax 3 + b
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Lhoussain El Fadil --- Sidi Mohamed Ben Abdellah University, MoroccoThe main goal of this paper is to provide a complete answer to the Problem 22 of Narkiewicz[24] for any quintic number field K generated by a complex root α of a monic irreducible trinomial F(x) = x 5 +... -
The significance of the contributions of congruences to the theory of connectednesses and disconnectednesses for topological spaces and graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Stefan Veldsman --- Nelson Mandela University, South AfricaThis is a survey of some of the consequences of the recently introduced congruences on the theory of connectednesses (radical classes) and disconnectednesses (semisimple classes) of graphs and topological spaces. In particular, it is shown that the connectednesses and disconnectednesses... -
Truncated vector lattices: A Maeda-Ogasawara type representation
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Karim Boulabiar --- Université de Tunis El Manar, Tunisia Rawaa Hajji --- Université de Tunis El Manar, TunisiaLet L be a truncated Archimedean vector lattice whose truncation is denoted by *. In a recent paper, we proved that there exists a locally compact Hausdorff space X such that L is a lattice isomorphic with a truncated vector... -
On property-(R 1) and relative Chebyshev centers in Banach spaces-II
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Syamantak Das --- Indian Institute of Technology Hyderabad, India Tanmoy Paul --- Indian Institute of Technology Hyderabad, IndiaWe continue to study (strong) property-(R 1) in Banach spaces. As discussed by Pai & Nowroji in [On restricted centers of sets, J. Approx. Theory, 66(2), 170–189 (1991)], this study corresponds to a triplet , where X is a Banach... -
When every regular ideal is S-finite
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mohamed Chhiti --- University S.M. Ben Abdellah Fez, Morocco Salah Eddine Mahdou --- University S.M. Ben Abdellah Fez, MoroccoIn this paper, we introduce a new class of ring called regular S-Noetherian ring, which is a weak version of S-Noetherian ring property. Any S-Noetherian ring is naturally a regular S-Noetherian ring, and in the domain context, these two forms... -
On mid (p, r)-compact operators
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Salthiel Malesela Maepa --- University of Pretoria, South Africa Brian Chihinga Ndumba --- University of Pretoria, South AfricaLet 1 ≤ p ≤ ∞ and 1 ≤ r ≤ p* where p* is the conjugate index of p. We introduce and study mid (p, r)-compact sets and operators. We begin by introducing and defining the mid (p, r)-compact... -
Index characterization and monogenity of septic number fields defined by x 7 + ax 4 + b
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Omar Kchit --- Sidi Mohamed ben Abdellah University, MoroccoIn this paper, we calculate the index of any septic number field K generated by a root α of a monic irreducible trinomial F(x) = x 7 + ax 4 + b ∈ ℤ[x]. Our approach is based on Engstrom’s... -
On graded-nonnil-Noetherian commutative rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Anass Assarrar --- University S.M. Ben Abdellah Fez, Morocco Najib Mahdou --- University S.M. Ben Abdellah Fez, MoroccoOur present work is motivated by several papers which have introduced and studied the notion of nonnil-Noetherian rings. Let A = ⊕ α ∈G A α be a commutative ring with unity graded by an arbitrary commutative monoid G... -
On z-ideals and z-closure operations of semirings, I
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Amartya Goswami --- University of Johannesburg, South AfricaThe aim of this series of papers is to study z-ideals of semirings. In this article, we introduce some distinguished classes of z-ideals of semirings, which include z-prime, z-semiprime, z-irreducible, and z-strongly irreducible ideals and study some of their properties... -
Lipschitz closed injective hull ideals and Lipschitz interpolative ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Rachid Yahi --- University of M’sila, University Pole, Algeria Dahmane Achour --- University of M’sila, University Pole, Algeria Elhadj Dahia --- University of M’sila, University Pole, AlgeriaIn this paper we present two constructions: the Lipschitz closed injective hull ideals and the Lipschitz interpolative ideals of a Lipschitz operator ideal. These procedures aim to construct new Lipschitz operator ideals between pointed metric spaces and Banach spaces. The... -
Banaschewski compactifications via special rings of functions in the absence of the Axiom of Choice
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Alireza Olfati --- Yasouj University, Iran Eliza Wajch --- University of Siedlce, PolandFor a topological space is the ring of all continuous real functions f on X such that, for every real number ϵ > 0, there exists a countable clopen cover of X such that the oscillation of f on each... -
A note on the construction of non-spatial frames
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Abolghasem Karimi Feizabadi --- Islamic Azad University, Iran Mahmoud Manafi --- Berlin College of Business and Technology (BCBT), Germany Inderasan Naidoo --- University of South Africa (UNISA), South AfricaWe introduce a new type of ideal, which we term a ζ-ideal (zeta-ideal), on a topological space. We present examples of ζ-ideals and study their properties. ζ-Ideals are shown to provide a new paradigm for constructing non-spatial frames. Beyond that,... -
Further remarks on z-ideals of semirings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Amartya Goswami --- University of Johannesburg, South Africa Ahmed Maatallah --- University of Monastir, Faculty of Sciences of Monastir, Research Laboratory on Algebra, TunisiaIn this note, we revisit certain results from a previous work of the first author concerning z-ideals of semirings. We demonstrate that the assumption of the semiring being a bzi-semiring can be dispensed with. Additionally, we propose a revised definition... -
On SVc -Spaces
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Amir Veisi --- Yasouj University, Iran Zahra Keshtkar --- Yasouj University, IranWe say that a topological space X is an SVc-space if Cc (X) is an SV - ring, that is, is a valuation ring for every prime ideal P of Cc (X). The purpose of this paper is to study... -
Remarks on the hilbert depth of monomial ideals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Silviu Bălănescu --- National University of Science and Technology Politehnica Bucharest, Romania Mircea Cimpoeaş --- National University of Science and Technology University Politehnica Bucharest, RomaniaLet K be a infinite field, S = K[x 1, …, xn ] and 0 ⊂ I ⊊ J ⊂ S two monomial ideals. In this note, we prove that if S/I is Cohen Macaulay, then hdepth (I) ≥ hdepth... -
An infinite family of number fields arising from quadrinomials with given p-indices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Omar Kchit --- Sidi Mohamed ben Abdellah University, MoroccoLet be a number field defined by a monic irreducible quadrinomial , where n > m > 1 are positive integers. In this paper, for any prime number p and for some fixed positive integers ip , we provide infinite... -
On quotient rings of pointfree function rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Batsile Tlharesakgosi --- University of South Africa, South Africa Sharon Nyokabi Wamugunda --- University of South Africa, South AfricaLet L be a completely regular frame. Associated with each I ∈ βL are two ideals, MI and OI , of the ring of real-valued continuous functions on a frame L. In this paper, we describe the intersection of all...