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Rings whose cyclics are U-modules
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-10-12 , DOI: 10.1142/s0219498822500074 Yasser Ibrahim 1, 2 , M. Tamer Koşan 3 , Truong Cong Quynh 4 , Mohamed Yousif 5
Journal of Algebra and Its Applications ( IF 0.5 ) Pub Date : 2020-10-12 , DOI: 10.1142/s0219498822500074 Yasser Ibrahim 1, 2 , M. Tamer Koşan 3 , Truong Cong Quynh 4 , Mohamed Yousif 5
Affiliation
A right R -module M is called a U -module if, whenever A and B are submodules of M with A ≅ B and A ∩ B = 0 , there exist two direct summands K and T of M such that A ⊆ ess K , B ⊆ ess T and K ⊕ T ⊆ ⊕ M . The class of U -modules is a strict and simultaneous generalization of quasi-continuous, square-free and automorphism-invariant modules. In this paper we study the rings whose cyclics are U -modules, extending many of the known results on the subject and providing new ones.
中文翻译:
循环是 U 模的环
一个权利R -模块米 被称为ü -模块如果,无论何时一种 和乙 是的子模块米 和一种 ≅ 乙 和一种 ∩ 乙 = 0 , 存在两个直接和ķ 和吨 的米 这样一种 ⊆ 埃斯 ķ ,乙 ⊆ 埃斯 吨 和ķ ⊕ 吨 ⊆ ⊕ 米 . 类ü -modules 是对准连续、无平方和自同构不变模块的严格同时推广。在本文中,我们研究环的环是ü -模块,扩展了该主题的许多已知结果并提供了新结果。
更新日期:2020-10-12
中文翻译:
循环是 U 模的环
一个权利