EP元的一些等价刻画  

Some equivalent characterizations on EP elements

作　　者：官梦鸽 周海楠 魏俊潮[1] GUAN Mengge;ZHOU Hainan;WEI Junchao(College of Mathematical Science,Yangzhou University,Yangzhou 225002,Jiangsu,China)

机构地区：[1]扬州大学数学科学学院,江苏扬州225002

出　　处：《山东大学学报（理学版）》2023年第8期13-17,共5页Journal of Shandong University(Natural Science)

摘　　要：研究分析EP元的性质,并将其与幂等元、Jacobson根结合给出EP元的一些等价刻画;又给出一个新结构方便系统地通过Moore-Penrose(MP)逆元、群逆元之间的关系等价刻画EP元;最后构建一些环上方程在特定集合上有解去等价刻画EP元。By studying the properties of EP elements and their association with idempotents and Jacobson radicals,some equivalent characterizations of EP elements are presented.A new structure is introduced to facilitate the equivalent characterizations of EP elements through Moore-Penrose(MP)inverses and the relationship between group inverses.Finally,by constructing some equations on the ring,the equivalent characterizations of EP elements are established by finding solutions on specific sets.

关 键 词：EP元 Moore-Penrose可逆元 群逆元 对合环 

分 类 号：O153.3[理学—数学]