T-nilpotence and preradicals
Copyright policy )T-nilpotence and preradicals
The T-nilpotence of an ideal K of a ring R is described by means of the left exact preradical Hom(R/K, ). The concept of essential extensions for preradicals is introduced and it is shown that a radical has no proper essential preradical extensions. Finally, as an application, a very simple proof of the generalized Nakayama lemma, together with a partial converse, is given.
- University of Guelph Canada
radical, Nil and nilpotent radicals, sets, ideals, associative rings, T-nilpotence, generalized Nakayama lemma, Centralizing and normalizing extensions, Radicals and radical properties of associative rings, Homological dimension in associative algebras, ideal, left exact preradical, essential extensions for preradicals, Modules, bimodules and ideals in associative algebras
radical, Nil and nilpotent radicals, sets, ideals, associative rings, T-nilpotence, generalized Nakayama lemma, Centralizing and normalizing extensions, Radicals and radical properties of associative rings, Homological dimension in associative algebras, ideal, left exact preradical, essential extensions for preradicals, Modules, bimodules and ideals in associative algebras
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