A New Class of Partial Orders  

作　　者：Huihui Zhu Liyun Wu 

机构地区：[1]School of Mathematics,Hefei University of Technology,Hefei 230009,China

出　　处：《Algebra Colloquium》2023年第4期585-598,共14页代数集刊（英文版）

基　　金：The authors are highly grateful to the referees for their valuable comments and suggestions which greatly improved this paper.This research is supported by the National Natural Science Foundation of China(No.11801124);China Postdoctoral Science Foundation(No.2020M671068).

摘　　要：Let R be a unital*-ring.For any a,w,b∈R,we apply the w-core inverse to define a new class of partial orders in R,called the w-core partial order.Suppose that a,b∈R are w-core invertible.We say that a is below b under the w-core partial order if a_(w)^(#)a=a_(w)^(#)b and a_(w)a_(w)^(#)=bwa_(w)^(#),where a_(w)^(#)denotes the w-core inverse of a.Characterizations of the w-core partial order are given,and its relationships with several types of partial orders are also considered.In particular,we show that the core partial order coincides with the a-core partial order,and the star partial order coincides with the a*-core partial order.

关 键 词：w-core inverse inverse along an element sharp partial order star partial order core partial order rings with involution 

分 类 号：O153.1[理学—数学]