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

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International Electronic Journal of Algebra
Volume:24 Issue:24
A NOTE ON MAL`TSEV-NEUMANN PRODUCTS OF RADICAL CLASSES

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

Pages : 1-11

View : 42 | Download : 12

Publication Date : 2018-07-05

Article Type : Research Paper

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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