JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 20-24.doi: 10.6040/j.issn.1671-9352.0.2024.192

• Group Theory • Previous Articles    

On the idempotent rank of the semigroup P On,r

RUAN Limin, GOU Changsheng, ZHAO Ping*   

  1. School of Mathematics Science Guizhou Normal University, Guiyang 550025, Guizhou, China
  • Published:2025-05-19

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Abstract: Let P On be the semigroup of all order-preserving partial transformation on Xn={1,2,…,n}. For 1≤r≤n, putP On,r={α∈P On:xα=x,∠x∈dom(α)∩{1,2,…,r}}.It is easy to check that the semigroup P On,r is subsemigroup of P On. In this paper, we prove that P On,r is generated by idempotents and its idempotent rank is equal to 3n-2r-1.

Key words: order-preserving partial transformation semigroup, fixed set, idempotent, idempotent rank

CLC Number: 

  • O152
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