Mod-Retractable Rings |
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| Authors: | M Tamer Koşan Jan Žemlička |
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| Institution: | 1. Department of Mathematics , Gebze Institute of Technology , Gebze – Kocaeli , Turkey mtkosan@gyte.edu.tr;3. Department of Algebra, Faculty of Mathematics and Physics , Charles University , Prague , Czech Republic |
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| 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 ? 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. |
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| Keywords: | Group module Max rings Noetherian rings Nonsingular rings Perfect rings Retractable module Semiartinian rings |
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