QUASI-IQC-INJECTIVITY

Samir M. Saied

Samir M. Saied Department of Mathematics, The Ministry of Education Directorate General for Education in Wasit, Iraq

Keywords: Quasi -injective modules, IQC -injective R-module, Quasi- closed submodules, fully continuous modules, divisible modules.

Abstract

In this work, the notion of injectivity relative to a class of IQC sub modules (namely, IQC-injectivity) has been introduced and studied, which is a generalization quasi-injective module. This notion is closed under direct summands. Several properties and characterizations have been given.We provide a characterization of semi simple Artinian ring , SI-ring and Dedekind domain in terms of IQC-injective R-module.

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