On (Semi)Regular Morphisms

Quynh, Truong Cong; Koşan, M. Tamer; Thuyet, Le Van

doi:10.1080/00927872.2012.667855

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Cited by 6 publications

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“…A module M is said to have the summand sum property if the sum of any two direct summands is a direct summand of M . These properties have been studied by several authors (see [1,3,11,12,17],...). Moreover, the classes of C3-modules and D3-modules have recently studied by Yousif et al in [4,20].…”

Section: Introduction and Notationmentioning

confidence: 99%

On classes of C3 and D3 modules

Abyzov¹

2017

HJMS

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This paper aims to study the notions of A-C3 and A-D3 modules for some class A of right modules. Several characterizations of these modules are provided and used to describe some well-known classes of rings and modules. For example, a regular right R-module F is a V -module if and only if every F -cyclic module is an A-C3 module, where A is the class of all simple right R-modules. Moreover, let R be a right artinian ring and A, a class of right R-modules with a local ring of endomorphisms, containing all simple right R-modules and closed under isomorphisms. If all right R-modules are A-injective, then R is a serial artinian ring with J 2 (R) = 0 if and only if every A-C3 right R-module is quasi-injective, if and only if every A-C3 right R-module is C3.

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