JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (10): 7-11.doi: 10.6040/j.issn.1671-9352.0.2016.471

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Maximal(regular)subsemigroups of the semigroup W(n,r)

LUO Yong-gui   

  1. School of Mathematics Science, Guizhou Normal University, Guiyang 550001, Guizhou, China
  • Received:2016-10-20 Online:2017-10-20 Published:2017-10-12

Abstract: Let RWn be the semigroup of all regular order-preserving and compressing singular transformations on a finite-chain[n] if n≥3, and let W(n,r)={α∈RWn:|Im(α)|≤r} be the two-sided ideal of the semigroup RWn for an arbitrary integer r accord with 1≤r≤n-1. By analyzing the elements of rank r and Greens relations, the classification of the maximal(regular)subsemigroup of the semigroup W(n,r) is completely obtained.

Key words: regular compression, order-preserving, maximal(regular)subsemigroup, singular transformation semigroup, complete classification

CLC Number: 

  • O152.7
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