右$c$-群逆及其应用

Right $c$-Group Inverses and Their Applications

中文关键词:  右-群逆  群逆  右-正则元素  强clean分解

英文关键词:right $c$-group inverse  group inverse  right $c$-regular elements  strongly clean decomposition

中文摘要:

      研究了由右$c$-正则元确定的一类新的群逆，将之称为右$c$-群逆.证明了每个右$c$-群可逆元都是群可逆的,并通过反例说明了群可逆元未必是右$c$-群可逆的.给出了右$c$-群可逆元是群可逆元的条件,并对右$c$-群可逆元的强clean分解进行了研究.作为应用,从右$c$-群逆的角度对abelian环和直接有限环给出了一些新刻画.

英文摘要:

      We study a new class of group inverses determined by right $c$-regular elements. The new concept of right $c$-group inverses is introduced and studied. It is shown that every right $c$-group invertible element is group invertible, and an example is given to show that group invertible elements need not be right $c$-group invertible. The conditions that right $c$-group invertible elements are precisely group invertible elements are investigated. We also study the strongly clean decompositions of right $c$-group invertible elements. As applications, we give some new characterizations of abelian rings and directly finite rings from the point of view of right $c$-group inverses.