J4 ›› 2016, Vol. 1 ›› Issue (6): 1-3.

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The Structure of the Completely Regular Semigroup in Dn

  

  1. (College of Mathematics and Computer, Dali University, Dali, Yunnan 671003, China)
  • Received:2015-11-26 Online:2016-06-15 Published:2016-06-15

Abstract:

This paper achieves the structure of completely regular semigroup through the investigation of completely regular elements
in doubly-stochastic matrix semigroup Dn. Namely,(CR)n ={PE|P ∈ ∩E ∈BnGE,E ∈Bn ⊆E(Dn)} is completely regular semigroup if and only
if Bn is a semi-lattice.

Key words: regular, completely regular element, idempotent, permutation matrix

CLC Number: