Email this article On generalizations of ADS modules and rings
- Authors: Hai P.T.1
-
Affiliations:
- Department of Mathematics
- Issue: Vol 37, No 3 (2016)
- Pages: 323-332
- Section: Article
- URL: https://journals.rcsi.science/1995-0802/article/view/197801
- DOI: https://doi.org/10.1134/S1995080216030227
- ID: 197801
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Abstract
A rightmodule M over a ring R is said to be ADSif, for every decomposition M = S ⊕ T and every complement T' of S, we have M = S ⊕ T'. In this article, we study and provide several new characterizations of new class of essential modules and generalization of ADS modules. We prove that M is semisimple if and only if every module in σ[M] is generalized ADS if and only if every generalized ADS module in σ[M] is M-injective.
About the authors
P. T. Hai
Department of Mathematics; Department of Mathematics
Author for correspondence.
Email: haikien2004@yahoo.com.vn
Viet Nam, Hue University 34 Le Loi, Hue City; Baria City, Baria-Vungtau province
