C<em>3</em>-Modules

• 作者: Ismail Amin Mohamed Yousif Yasser Ibrahim
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 类模块 自内射环 连续性条件 不可分解 直和项 内射模 交换环 半单
• 年，卷（期）: 2015,（4）
• 页码范围: 655-670
• 页数: 16页
• 分类号: O153.3
• 语种: 中文

摘要

One of the continuity conditions identified by Utumi on self-injective rings is the C3-condition, where a module M is called a C3-module if whenever A and B are direct summands of M and A A B = 0, then A B is a summand of M. In addition to injective and direct-injective modules, the class of C3-modules includes the semisimple, continuous, indecomposable and regular modules. Indeed, every commutative ring is a C3-ring. In this paper we provide a general and unified treatment of the above mentioned classes of modules in terms of the C3-condition, and establish new characterizations of several well known classes of rings.