On A Class of Soc-Injective Modules

Message:
Article Type:
Research/Original Article (دارای رتبه معتبر)
Abstract:

Let R be a ring. The class of SA-injective right R-modules (SAIR) is introduced as a class of soc-injective right R-modules. Let N be a right R-module. A right R-module M is said to be SA-N-injective if every R-homomorphism from a semi-artinian submodule of N into M extends to N. A module M is called SA- njective, if M is SA-R-injective. We characterize rings over which every right module is SA-injective. Conditions under which the class SAIR is closed under uotient (resp. directsums, pure homomorphic images) are given. The definability of the class SAIR is studied. Finally, relations between SA-injectivity and certain generalizations of injectivity are given.

Language:
English
Published:
Iranian Journal of Mathematical Sciences and Informatics, Volume:18 Issue: 2, Nov 2023
Pages:
51 to 65
https://www.magiran.com/p2630318