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Published: 2017-10-30

Page: 110-115


Department of Mathematics, Faculty of Sciences and Arts, Amasya University, Amasya, Turkey

*Author to whom correspondence should be addressed.


Let R be an arbitrary ring and M be a left R-module. is called P-supplemented if every submodule N of M with P(M) ⊆ N has a supplement in M, where P(M) is the sum of all submodules of M such that N = Rad(N). In this paper, the basic properties of these modules are investigated as a proper generalization of supplemented modules. In particular, it is shown that a ring R is (semi) perfect if and only if every left ( nitely generated) R-module is P-supplemented. Moreover, the structure of P-supplemented modules over Dedekind domains is completely determined. Also, Rad-supplemented modules are characterized in terms of P-supplemented modules over Dedekind domains.

Keywords: Radical submodule, supplement, Rad-supplement, (semi) perfect ring

How to Cite

TÜRKMEN, E. (2017). P-SUPPLEMENTED MODULES. Asian Journal of Mathematics and Computer Research, 21(3), 110–115. Retrieved from https://ikprress.org/index.php/AJOMCOR/article/view/1140


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