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- Title
Modules that Have a δ-supplement in Every Extension.
- Authors
Sözen, Esra Öztiirk; Eren, Şenol
- 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 Zöschinger'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 prove that if R is a δ-perfect ring then every left R-module has the property (δ-E). Moreover, the converse is also true on δ-semiperfect rings.
- Subjects
RING extensions (Algebra); MODULES (Algebra); GENERALIZATION; EXPONENTIAL sums; MATHEMATICAL proofs
- Publication
European Journal of Pure & Applied Mathematics, 2017, Vol 10, Issue 4, p730
- ISSN
1307-5543
- Publication type
Article