A factorization of dual prehomomorphisms and expansions of inverse semigroups

ISSN： 0081-6906

Source： Studia Scientiarum Mathematicarum Hungarica, Vol.41, Iss.3, 2004-08, pp. : 295-308

Disclaimer: Any content in publications that violate the sovereignty, the constitution or regulations of the PRC is not accepted or approved by CNPIEC.

Previous Menu Next

Abstract

For any inverse semigroup S we construct an inverse semigroup S(S), which has the following universal property with respect to dual prehomomorphisms from S: there is an injective dual prehomomorphism &igr;_S: S → S(S) such that for each dual prehomomorphism θ from S into an inverse semigroup T there exists a unique homomorphism θ*: S(S) →to T with &igr;_S θ* = θ. If we restrict the class of dual prehomomorphisms under consideration to order preserving ones, S(S) may be replaced by a certain homomorphic image ŝ(S) which can be viewed as a natural generalization of the Birget--Rhodes prefix expansion for groups [4] to inverse semigroups. Recently, Lawson, Margolis and Steinberg [8] have given an alternative description of ŝ(S) which is based on O'Carroll's theory of idempotent pure congruences [11]. It should be noted that our ideas can be used to simplify some of their arguments.