Modules that Have a δ-Supplement in Every Extension

Authors

  • Esra Ozturk Sozen Ondokuz Mayis University
  • Åženol Eren

Keywords:

Supplement, δ-supplement, δ-perfect ring, module extension

Abstract

Let R be a ring and M be a left R-module. In this paper, we define modules with the properties (δ-E) and (δ-EE), which are generalized version of Zoschinger's modules with the properties (E) and (EE) , and provide various properties of these modules. We prove that the class of modules with the property (δ-E) is closed under direct summands and finite direct sums.It is shown that a module M has the property (δ-EE) if and only if every submodule of M has the property (δ-E). It is a known fact that a ring R is perfect if and only if every left R-module has the property (E). As a generalization of this, we also prove that a ring R is δ-perfect if and only if every left R-module has the property (δ-E).

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Published

2017-07-11

Issue

Vol. 10 No. 4: (July 2017)

Section

Econometrics and Forecasting

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How to Cite

Modules that Have a δ-Supplement in Every Extension. (2017). European Journal of Pure and Applied Mathematics, 10(4), 730-738. https://www.ejpam.com/index.php/ejpam/article/view/3024