E. Ochmanski and P.-A. Wacrenier

Regular morphisms on semicommutations

850

Abstract

Each semicommutation defines the family of all closed and regular subsets of A*. Let A* and B* be two semi-commutations. A morphism is said to be regular if and only if it preserves regularity of subsets. A characterization of regular semi-commutations (the case A=B and f=id was given in [OW93]. In this paper we prove regularity of some special class of morphisms - path-preserving morphisms. Using this result and the former characterization of regular semicommutations we obtain a criterion of regularity for the class of injective morphisms. Finally, we prove quite weak sufficient condition of regularity for arbitrary morphisms. We do not know, if the condition is also a necessary one.

Key words: semi-commutation, morphism, regular set.