Asian Journal of Mathematics and Computer Research
 

Asian Journal of Mathematics and Computer Research, ISSN No. : 2395-4205 (Print), 2395-4213 (Online), Vol.: 21, Issue.: 3

Short Research Article

P-SUPPLEMENTED MODULES

 

ERGÜL TÜRKMEN1*
1Department of Mathematics, Faculty of Sciences and Arts, Amasya University, Amasya, Turkey.

Abstracts

Let R be an arbitrary ring and M be a left R-module. M 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 N 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.