Abstract
Denote by T(X)the semigroup of full transformations on a set X.F or! T(X) ,t he centralizer of! is a subsemigroup of T(X)defined by C(!) ={ T(X): = ! } .I t is well known thatC(idX) = T(X)is a regular semigroup. By a theorem proved by J.M. Howie in 1966, we know that if X is finite, then the subsemigroup generated by the idempotents of C(idX) contains all non-invertible transformations in C(idX). This paper generalizes this result to C(!) ,a n arbitrary regular centralizer of an idempotent transformation T(X) ,b y describing the subsemigroup generated by the idempotents of C(!) .A s ac orollary we obtain that the subsemigroup generated by the idempotents of a regular C(!) contains all non-invertible transformations in C(!) if and only if is the identity or a constant transformation.
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