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|Title:||Semigroups of transformations with fixed sets|
|Abstract:||Let T (X) denote the semigroup (under composition) of transformations from X into itself. For a fixed subset Y of X, let Fix(X, Y) be the set of all self-maps on X which fix all elements in Y. Then Fix(X, Y) is a regular subsemigroup of T (X). The aim of this paper is to determine the Green's relations and ideals of Fix(X, Y) and prove that Fix(X, Y) is never isomorphic to T (Z) for any set Z when ∅ ≠ Y ⊈ X. However, its rank is related to the rank of T (X\Y) and the cardinality of Y when X is a finite set. © 2013 Copyright NISC Pty Ltd.|
|Appears in Collections:||CMUL: Journal Articles|
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