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 ⊆essK, B ⊆essT 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：

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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。