S_n中元素的左、右逆的研究

The study of the left and right inverse of elements in S_n

[1]对次随机矩阵半群的正则元作了研究。文章将对随机矩阵半群中元的随机左、右逆进行了探讨。首先给出了Sn中元有随机右逆的充要条件以及元有唯一随机右逆的充要条件,其次,给出了Sn中元有随机左逆的充要条件。本文在最后给出了比Sn更广的一类半群T,它的幂等元、正则元就是Sn中的幂等元和正则元。

In the regular elements of semigroup φ_n of substochastic matrices have been studied. This paper investigates the left and right inverse of elements in S_n of stochastic matrices. Firstly we give necessary and sufficient conditions that element in S_n has right inverse or left inverse and that element in S_n has unique right inverse. Finally we give a semigroup T that S_n is its subsemigroup and which regular and idempotent elements are in S_n.