Journal of Algebra and Its Applications ( IF 0.8 ) Pub Date : 2021-06-19 , DOI: 10.1142/s0219498822501870 Sanjeev Kumar Maurya 1 , Sultan Eylem Toksoy 2
In this paper, we have introduced copure-direct-injective modules. A right -module is said to be copure-direct-injective if every copure submodule of isomorphic to a direct summand of is itself a direct summand. We have studied properties of copure-direct-injective modules. We characterized rings over which every (cofinitely generated, free, projective) module is copure-direct-injective. We have examined for which rings or under what conditions copure-direct-injective modules are direct-injective, quasi-injective, copure-injective, injective. Also we have compared copure-direct-injective modules with pure-direct-injective modules.
中文翻译:
Copure 直射模块
在本文中,我们介绍了 copure-direct-injective 模块。一个权利-模块如果每个 copure 子模同构于的直接和本身就是一个直接的要求。我们研究了 copure-direct-injective 模块的性质。我们对环进行了表征,在该环上,每个(有限生成的、自由的、投射的)模块都是 copure-direct-injective。我们已经检查了哪些环或在什么条件下 copure-direct-injective 模块是直接内射、准内射、copure-injective、内射。我们还比较了 copure-direct-injective 模块和 pure-direct-injective 模块。