J4 ›› 2011, Vol. 46 ›› Issue (4): 75-77.

• Articles • Previous Articles     Next Articles

Idempotent rank in decreasing and order-preserving finite partial transformation semigroups

ZHAO Ping1, YOU Tai-jie2, XU Bo2, HU Hua-bi1   

  1. 1. School of Basic Medicine, Guiyang Medical College, Guiyang 550004, Guizhou, China;
    2. School of Mathematics and Computer Science, Guizhou Normal University, Guiyang 550001, Guizhou,  China
  • Received:2010-04-26 Published:2011-04-21


Let PCn be the semigroup of all decreasing and order-preserving partial transformations on [n]. For n≥3, we shall show that the semigroup PCn is generated by idempotents of rank n-1, and that its rank and idempotent rank are both equal to 2n-1.

Key words:  transformation semigroup; decreasing; order-preserving; idempotent rank; rank

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