Elementary radical classes

Year 2018, Volume: 23 Issue: 23, 25 - 41, 11.01.2018

B. J. Gardner

https://doi.org/10.24330/ieja.373634

Cited By: 1

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. Attention is

given to those elementary radical classes which are denable by composition

subsemigroups of the free ring on one generator. Whether every elementary

radical class is of this form remains an open question.

Keywords

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

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