PORTUGALIAE MATHEMATICA Vol. 51, No. 2, pp. 185204 (1994) 

On the Idempotent Ranks of Certain Semigroups of OrderPreserving TransformationsG.U. GarbaDepartment of Mathematical and Computational Sciences,University of St Andrews, Scotland  U.K. and Department of Mathematics, Ahmadu Bello University Zaria  NIGERIA Abstract: The ranks of the semigroups $O_{n}$, $PO_{n}$ and $SPO_{n}$ (the semigroups of orderpreserving singular selfmaps, partial and strictly partial transformations on $X_{n}=\{1,...,n\}$ respectively), and the idempotent ranks of $O_{n}$ and $PO_{n}$ were studied by Gomes and Howie [2]. In this paper we generalize their results in line with Howie and McFadden [7], by considering the semigroups $L(n,r)$, $M(n,r)$ and $N(n,r)$, where, for $2\le r\le n2$, $L(n,r)=\{\alpha\in O_{n}:\IM\alpha\le r\}$, $M(n,r)=\{\alpha\in PO_{n}:\IM\alpha\le r\}$ and $N(n,r)=\{\alpha\in SPO_{n}:\IM\alpha\le r\}$. Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1994 Sociedade Portuguesa de Matemática
