J4 ›› 2013, Vol. 48 ›› Issue (12): 70-74.

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Non-group rank and relative rank of the semigroup W(n,r)

LUO Yong-gui   

  1. Department of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, Guizhou, China
  • Received:2013-03-05 Online:2013-12-20 Published:2014-01-09

Abstract:

Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain [n]. For an arbitrary integer r(2≤r≤n-1), the non-group rank and non-idempotent rank of the semigroup W(n,r)={α∈RWn:|Imα|≤r} were studied. The semigroup W(n,r) generated by elements of rank r is proved. Furthermore, it is shown that for 1≤l≤r, the relative rank of the semigroup W(n,r) with respect to itself each ideal W(n,l).

Key words: order-preserving; compression; singular transformation semigroup; non-group rank and non-idempotent rank; relative rank

CLC Number: 

  • O152.7
[1] ZHANG Xiao-Min. Wreath products structure of super R*-unipotent semigroups [J]. J4, 2009, 44(9): 66-69.
[2] BI Xiao-Dong. Tensor product of left quasinormal bands [J]. J4, 2009, 44(8): 39-41.
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