(g,e)-Symmetric Rings  

作　　者：Fanyun Meng Junchao Wei Nanqing Ding 

机构地区：[1]School of Mathematics,Yangzhou University,Yangzhou,Jiangsu 225002,China [2]不详

出　　处：《Algebra Colloquium》2024年第2期263-270,共8页代数集刊（英文版）

基　　金：supported by the Foundation of Natural Science of China(12301029,11171291);Natural Science Fund for Colleges and Universities in Jiangsu Province(11KJB110019 and 15KJB110023).

摘　　要：Let R be a ring and e,g in E(R),the set of idempotents of R.Then R is called(g,e)-symmetric if abc=0 implies gacbe=0 for any a,b,c∈R.Clearly,R is an e-symmetric ring if and only if R is a(1,e)-symmetric ring;in particular,R is a symmetric ring if and only if R is a(1,1)-symmetric ring.We show that e∈E(R)is left semicentral if and only if R is a(1−e,e)-symmetric ring;in particular,R is an Abel ring if and only if R is a(1−e,e)-symmetric ring for each e∈E(R).We also show that R is(g,e)-symmetric if and only if ge∈E(R),geRge is symmetric,and gxye=gxeye=gxgye for any x,y∈R.Using e-symmetric rings,we construct some new classes of rings.

关 键 词：IDEMPOTENT (g e)-symmetric ring Abel ring left semicentral 

分 类 号：O17[理学—数学]