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On Polynomial and Multiplicative Radicals
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: S. Tumurbat R. WiegandtWe show that polynomial and multiplicative radicals in [1] are special cases of radicals defined by means of elements. We scrutinize the way of defining a radical γG by a subset G of polynomials in noncommuting indeterminates. Defining polynomial radicals,... -
A generalization of 2-primal near-rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: N. Argac N.J. GroenewaldIn this note we generalize the notion of 2-primal and nil-primal nearrings. For a Hoehnke radical ρ we introduce the notion of ρ–primal near-rings. 2-primal and nil-primal near-rings are examples of ρ–primal near-rings. We show that many of the results... -
Different nil radicals for near-rings
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: N.J GroenewaldIt is well known that there are a number of different nonequivalent definitions of a prime near-ring. In this paper we show that this give rise to a number of different upper nil radicals which all coincide with the usual... -
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...