نشریه علوم ریاضی و انفورماتیک

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Ramadan Mehdi A. On A Class of Soc-Injective Modules. IJMSI 2023; 18 (2) :51-65
URL: http://ijmsi.ir/article-1-1626-fa.html

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.