C3-Modules  

作　　者：Ismail Amin Yasser Ibrahim Mohamed Yousif 

机构地区：[1]Department of Mathematics, Faculty of Science Cairo University, Giza, Egypt [2]Department of Mathematics, The Ohio State University Lima, Ohio 45804, USA

出　　处：《Algebra Colloquium》2015年第4期655-670,共16页代数集刊（英文版）

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.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.

关 键 词：injective and quasi-injective modules C2-modules and C3-modules 

分 类 号：O153.3[理学—数学] TP311[理学—基础数学]