Centralisers in the infinite symmetric inverse semigroup

Authors

  • Janusz Konieczny University of Mary Washington

Keywords:

symmetric inverse semigroup, centralizers, regular elements, Green's relations

Abstract

For an arbitrary set X (finite or infinite), denote by I(X) the symmetric inverse semigroup of partial injective transformations on X. For an element a in I(X), let C(a) be the centralizer of a in I(X). For an arbitrary a in I(X), we characterize the elements b in I(X) that belong to C(a), describe the regular elements of C(a), and establish when C(a) is an inverse semigroup and when it is a completely regular semigroup. In the case when the domain of a is X, we determine the structure of C(a) in terms of Green's relations. 10.1017/S0004972712000779

Author Biography

Janusz Konieczny, University of Mary Washington

Professor of Mathematics

Published

2013-04-29

Issue

Section

Articles