In this paper, the notion of “strongly unit regular element”, for which every reflexive generalized inverse is associated with an inverse complement, is introduced. Noting that every strongly unit regular element is unit regular, some characterizations of unit regular elements are obtained in terms of inverse complements and with the help of minus partial order. Unit generalized inverses of given unit regular element are characterized as sum of reflexive generalized inverses and the generators of its annihilators. Surprisingly, it has been observed that the class of strongly regular elements and unit regular elements are the same. Also, several classes of generalized inverses are characterized in terms of inverse complements.

本文介绍了“强单位正则元”的概念，其中每一个自反广义逆都与一个逆补相关联。注意到每个强单位正则元素都是单位正则，单位正则元素的一些表征是根据逆补和借助负偏序获得的。给定单位正则元素的单位广义逆被表征为自反广义逆及其湮没子的生成元之和。令人惊讶的是，已经观察到强正则元素和单位正则元素的类别是相同的。此外，几类广义逆是用逆补来表征的。