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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. -
Derivations on Functional (Local Banach) Algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. KhosraviFirstly we obtain some of the general properties of functional (local Banach) algebras and secondly we generalize some of the known results of derivations on Banach algebras to such algebras. -
Generalized Derivations of Associative Algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Hiroaki Komatsu Atsushi NakajimaIn their paper [6], Leger and Luks introduced the notion of a generalized derivation in nonassociative algebras and got several results for generalized derivations of Lie algebras. This generalized derivation is closely related to Breˇsar's and the second author's generalized... -
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... -
Positive derivations on lattice ordered rings of matrices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Homeira PajooheshHere we consider a commutative ℓ-ring R with unit. We show that the only positive derivation on the ℓ-ring Mn (R) is 0 if and only if the only positive derivation on R is zero. Also, if the only positive... -
On Prime and Semiprime Near-Rings with Generalized Derivation
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Öznur Gölbaşi --- Department of Mathematics, TurkeyLet N be a left near-ring and S be a nonempty subset of N. A mapping F from N to N is called commuting on S if [F(x),x] = 0 for all x € S. The mapping F is called... -
Symmetric bi-derivations of lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Yılmaz ÇevenIn this paper, we introduced the notion of symmetric bi-derivation on lattices and investigated some related properties. We characterized the distributive and modular lattices by symmetric bi-derivations. -
Permuting tri-derivations in lattices
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Mehmet Ali Öztürk --- Faculty of Arts and Sciences, Department of Mathematics, Turkey Hasret Yazarli --- Faculty of Arts and Sciences, Department of Mathematics, Turkey Kyung Ho Kim --- Department of Mathematics, KoreaThe aim of this paper is to introduce the notion of permuting triderivations in lattices and to study some properties of permuting tri-derivations. -
Lie triple centralizers on generalized matrix algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Behrooz Fadaee --- University of Kurdistan, Iran Hoger Ghahramani --- University of Kurdistan, Iran Wu Jing --- Fayetteville State University, USAIn this article, we introduce the notion of Lie triple centralizer as follows. Let be an algebra, and be a linear mapping. We say that ϕ is a Lie triple centralizer whenever for all . Then we characterize the general... -
Non-existence of translation-invariant derivations on algebras of measurable functions
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Aleksey Ber --- National University of Uzbekistan, Uzbekistan Jinghao Huang --- University of New South Wales, Australia Karimbergen Kudaybergenov --- Karakalpak State University, Uzbekistan Fedor Sukochev --- University of New South Wales, AustraliaLet S(0,1) be the *-algebra of all classes of Lebesgue measurable functions on the unit interval (0,1) and let be a complete symmetric Δ-normed *-subalgebra of S(0,1), in which simple functions are dense, e.g., L ∞(0,1), L log(0,1), S(0,1) and... -
A characterization of derivations of JSL algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Lin Chen --- Changshu Institute of Technology, P.R. China Jun Li --- Changshu Institute of Technology, P.R. ChinaChina Zijie Qin --- Changshu Institute of Technology, P.R. ChinaChinaLet be a -subspace lattice algebra on a Banach space X and Inv() be the set of all invertible elements of . Suppose that δ : → is a linear mapping satisfying δ(A) ◦ A −1 + A ◦ δ(A... -
Generalized Jordan derivable mappings on
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Kaijia Luo --- Institute of Mathematics, Hangzhou Dianzi University, China Jiankui Li --- School of Mathematics, East China University of Science and Technology, China Shanshan Su --- School of Mathematics, East China University of Science and Technology, ChinaLet be a Hilbert space over the real or complex field and be the algebra of all bounded linear operators on . For arbitrary fixed points C, D, M in , we investigate the structure of linear mappings δ and... -
Derivations in disjointly complete commutative regular algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Aleksey Ber --- National University of Uzbekistan, Uzbekistan Vladimir Chilin --- North-Ossetian State University, Russia Fedor Sukochev --- UNSW, AustraliaWe show that any nonexpansive derivation on a subalgebra of a dis-jointly complete commutative regular algebra extends up to a derivation on . For an algebra of functions , continuous on a dense open subset of Stone compact X, we... -
Lie derivable maps at unit operator on nest algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Kaipeng Li --- Xidian University, P.R. China Lei Liu --- Xidian University, P.R. ChinaLet be a nontrivial nest on a separable Hilbert space and be the associated nest algebra. In this note, we prove that, if contains an atom of infinite rank or is uncountable, then the unit operator I is a Lie... -
Super-skewsymmetric super-biderivations on the N = 1 super Heisenberg-Virasoro algebra
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jinlu Li --- Shanghai University, China Jiancai Sun --- Shanghai University, ChinaIn this paper, the super-skewsymmetric super-biderivations on the N = 1 super Heisenberg-Virasoro algebra are completely determined. Furthermore, we find that every super-skewsymmetric super-biderivation of the N = 1 super Heisenberg-Virasoro algebra is inner. -
Generalized derivations with nilpotent values in semiprime rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Cheng-Kai Liu --- National Changhua University of Education, TaiwanLet R be a (semi-) prime ring with extended centroid C, let f(X 1, … , Xk ) be a multilinear polynomial over C in k noncommutative indeterminates which is not central-valued on R and let g be a generalized derivation of... -
The second nonlinear mixed bi-skew Lie triple derivations on factor von Neumann algebras
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Yuan Yang --- Shaanxi Normal University, People’s Republic of China Jianhua Zhang --- Shaanxi Normal University, People’s Republic of ChinaLet be a factor von Neumann algebra with dim . In this paper, it is shown that if a map satisfies for all , then ϕ is an additive ∗-derivation, where . -
An overview of Xitsonga reduplication constructions
Item type: Journal Article • Journal: South African Journal of African Languages • Authors: Lebogang Steven Shirindzi --- University of Venda, South Africa Arnold Mushwana --- University of South Africa, South AfricaWord-formation processes leading to abbreviations such as clipping, blending and acronyms occur only partially, or do not occur at all, in Xitsonga. In constrast, one of the most productive word-formation processes in Xitsonga is reduplication. Several studies have been conducted...