具有*-IFP性质的*-半环  

*-semirings with *-IFP

作　　者：卓远帆 谷勤勤 周芯雨 ZHUO Yuanfan;GU Qinqin;ZHOU Xinyu(School of Mathematics and Physics,Anhui University of Technology,Maanshan,Anhui,243032,P.R.China;School of Mathematics Science,Yangzhou University,Yangzhou,Jiangsu,225002,P.R.China)

机构地区：[1]安徽工业大学数理科学与工程学院,马鞍山安徽243032 [2]扬州大学数学科学学院,扬州江苏225002

出　　处：《数学进展》2022年第5期860-872,共13页Advances in Mathematics（China）

基　　金：Supported by the Natural Science Foundation of Anhui Province(No.2008085QA03)。

摘　　要：本文研究了具有*-IFP性质的*-半环.称*-半环R具有*-IFP性质,如果对于任意的a∈R,a的右零化子是R的一个*-理想.这个定义等价于,对于任意的a,b∈R,由ab=0可推出aRb^(*)=0.我们对于这种*-半环的性质进行刻画,并给出了一些具体的例子.作为应用,我们主要研究了与这类*-半环相关的广义逆.对于加法可消、幂等元可补且具有*-IFP性质的*-半环R,如果a∈R是自反可逆的,则可以得到a是EP元、偏序等距元、正规元和强EP元的等价刻画.We study*-semirings with*-IFP.A*-semiring R has*-IFP if for every a∈R,the right annihilator of a is a*-ideal of R,which is equivalent that ab=0 implies aRb^(*)=0 for all a,b∈R.Some characterizations and examples of this class of semirings are given.As applications,generalized inverses related to*-semirings with*-IFP are studied.For an additive cancellative and Id-complemented*-semiring R having*-IFP,if a∈R is reflexive invertible,some equivalent characterizations of a being EP elements,partial isometries,normal elements and strong EP elements are given.

关 键 词：*-半环 对合 *-IFP 广义逆 

分 类 号：O153.3[理学—数学]