### Rank and relative rank of the semigroup PD(n,r)

ZHANG Qian-tao, LUO Yong-gui*, ZHAO Ping

1. School of Mathematics Science, Guizhou Normal University, Guiyang 550025, Guizhou, China
• Online:2020-10-20 Published:2020-10-07

Abstract: Let PDn 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∈PDn:|im(α)|≤r}(0≤r≤n-1)be the two-sided ideal of the semigroup PDn. By analyzing the elements with rank r of the semigroup PDn, 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.

CLC Number:

• O152.7
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