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MOD-RETRACTABLE RINGS

Publication at Faculty of Mathematics and Physics |
2014

Abstract

A right module M over a ring R is said to be retractable if Hom(R)(M, N)0 for each nonzero submodule N of M. We show that M circle times(R)RG is a retractable RG-module if and only if M-R is retractable for every finite group G.

The ring R is (finitely) mod-retractable if every (finitely generated) right R-module is retractable. Some comparisons between max rings, semiartinian rings, perfect rings, noetherian rings, nonsingular rings, and mod-retractable rings are investigated.

In particular, we prove ring-theoretical criteria of right mod-retractability for classes of all commutative, left perfect, and right noetherian rings.