A NOTE ON MAL'TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES

Year 2018, Volume: 24 Issue: 24, 1 - 11, 05.07.2018

B. J. Gardner

https://doi.org/10.24330/ieja.440117

Abstract

A radical class R of rings is elementary if it contains precisely

those rings whose singly generated subrings are in R. Many examples of ele-

mentary radical classes are presented, and all those which are either contained

in the Jacobson radical class or disjoint from it are described. There is a dis-

cussion of Mal'tsev products of radical classes in general, in which it is shown,

among other things, that a product of elementary radical classes need not be

a radical class, and if it is, it need not be elementary.

Keywords

Radical class, locally equational class, Mal'tsev-Neumann product

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