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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.
2010 Mathematics Subject Classification:
ACKNOWLEDGMENT
The authors would like to express their deep gratitude to the referee for a very careful reading of the article, and many valuable comments, which have greatly improved presentation of the article. The authors wish to thank Simion Breaz who formulated and proved Theorems 3.5 and 3.7 and improved the formulation of Lemma 3.17.
The second author is supported by research project MSM 0021620839, financed by M\v SMT.
Notes
Communicated by T. Albu.