摘要
给出ZP-内射模的概念,举例说明ZP-内射模是P-内射模的一类真推广,讨论该模的等价刻画和基本性质如:RM是ZP-内射模当且仅当对于环R的任意a∈Z(RR),rMlR(a)=aM;ZP-内射左R-模的纯子模是ZP-内射左R-模等.利用ZP-内射模刻画非奇异环即:R是左非奇异环当且仅当任意左R-模是ZP-内射模,当且仅当Z(RR)R,任意单左R-模是ZP-内射模,最后讨论一类特殊的ZP-内射模—ZP-内射环及其自反性.
In this paper,the notion of ZP-injective modules is defined. The examples show that the definition of ZP-injective modules is a proper generalization of that of P-injective modules. Then their equivalent definitions and basic properties are discussed. For example,RM is ZP-injective if and only if for any a∈Z（RR） of R,rMlR（ a） = aM; any pure submodule of a ZP-injective module is ZP-injective. By using ZP-injective modules,nonsingular rings are characterized. It is shown that the ring R is left nonsingular if and only if any left R-module is ZP-injective if and only if Z（RR）〈 R and any simple left R-module is ZP-injective. Finally,the reflexive properties of ZP-injective rings are discussed.
出处
《四川师范大学学报（自然科学版）》
CAS
北大核心
2015年第5期644-647,共4页
Journal of Sichuan Normal University（Natural Science）
基金
国家自然科学基金(11171240)
关键词
纯子模
ZP-内射模
ZP-内射环
非奇异环
pure submodules
ZP-injective modules
ZP-injective rings
nonsingular rings
