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RISS 인기검색어
- 검색키워드
- 저자 : ( Esra Öztürk Sözen ) (검색결과 2 건)
- 무료
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ON COFINITELY CLOSED WEAK δ-SUPPLEMENTED MODULES
( Esra Öztürk Sözen ) 호남수학회 2020 호남수학학술지 Vol.42 No.3
A module M is called cofinitely closed weak δ-supplemented (briey δ-ccws-module) if for any cofinite closed submodule N of M has a weak δ-supplement in M: In this paper we investigate the basic properties of δ-ccws modules. In the light of this study, we can list the main facts obtained as following: (1) Any cofinite closed direct summand of a δ-ccws module is also a δ-ccws module; (2) Let R be a left δ-V -ring. Then R is a δ-ccws module iff R is a ccws-module iff R is extending; (3) Any nonsingular homomorphic image of a δ-ccws-module is also a δ-ccws-module; (4) We characterize nonsingular δ-V -rings in which all nonsingular modules are δ-ccws.
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A RECENT GENERALIZATION OF COFINITELY INJECTIVE MODULES
( Esra Öztürk Sözen ) 호남수학회 2023 호남수학학술지 Vol.45 No.3
Let R be an associative ring with identity and M be a left R-module. In this paper, we define modules that have the property (δ- CE) ((δ-CEE)), these are modules that have a δ-supplement (ample δ- supplements) in every cofinite extension which are generalized version of modules that have the properties (CE) and (CEE) introduced in [6] and so a generalization of Zöschinger’s modules with the properties (E) and (EE) given in [23]. We investigate various properties of these modules along with examples. In particular we prove these: (1) a module M has the property (δ-CEE) if and only if every submodule of M has the property (δ-CE); (2) direct summands of a module that has the property (δ-CE) also have the property (δ-CE); (3) each factor module of a module that has the property (δ-CE) also has the property (δ-CE) under a special condition; (4) every module with composition series has the property (δ- CE); (5) over a δ-V -ring a module M has the property (δ-CE) if and only if M is cofinitely injective; (6) a ring R is δ-semiperfect if and only if every left R-module has the property (δ-CE).
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