Normal categories of semigroup of order-preserving transformations on a finite chain
Abstract
K. S. S. Nambooripad intoduced nornal categories to enable to describe the structure of regular semigroups fully. In this paper we describe the ideal categories of the regular semigroup OXn, of non-invertible order-preserving transformations on a finite chain Xn=\1≤ 2≤ ·s ≤ n \ which are normal categories. Further it is shown that the principal left ideal category of OXn as the power set category Po(Xn) of OXn and the principal right ideal category as Πo(Xn) category of ordered partitions of Xn and described the cone semigroup T L(OXn) and prove that it is isomorphic to OXn.
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