%A ZHANG Qian-tao, LUO Yong-gui, ZHAO Ping
%T Rank and relative rank of the semigroup PD(*n,r*)
%0 Journal Article
%D 2020
%J JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
%R 10.6040/j.issn.1671-9352.0.2019.922
%P 63-70
%V 55
%N 10
%U {http://lxbwk.njournal.sdu.edu.cn/CN/abstract/article_3349.shtml}
%8 2020-10-20
%X Let PD_{}*n* be the semigroup of all distance-preserving partial one-to-one singular transformations on a finite-chain ［*n］(n≥*3), and let PD(*n,r)={α*∈PD_{}*n*:|im*(α)|≤r}(*0*≤r≤n-*1)be the two-sided ideal of the semigroup PD_{}*n*. By analyzing the elements with rank *r* of the semigroup PD_{}*n*, the minimal generating set and rank of the semigroup PD(*n,r*)are obtained. Furthermore, the relative rank of the semigroup PD(*n,r*)with respect to its ideal PD(*n,l*)is determined for 0≤*l≤r*.