Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals
Permanent URI for this collection
Browse
Browsing Matemática e Estatística | Artigos em revistas internacionais / Papers in international journals by Author "André, Jorge"
Now showing 1 - 1 of 1
Results Per Page
Sort Options
- Regular centralizers of idempotent transformationsPublication . André, Jorge; Araújo, João; Konieczny, JanuszDenote by T(X) the semigroup of full transformations on a set X. For ε∈T(X), the centralizer of ε is a subsemigroup of T(X) defined by C(ε)={α∈T(X):αε=εα}. It is well known that C(id X )=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(id X ) contains all non-invertible transformations in C(id X ). This paper generalizes this result to C(ε), an arbitrary regular centralizer of an idempotent transformation ε∈T(X), by describing the subsemigroup generated by the idempotents of C(ε). As a corollary we obtain that the subsemigroup generated by the idempotents of a regular C(ε) contains all non-invertible transformations in C(ε) if and only if ε is the identity or a constant transformation.