Expansions, free inverse semigroups, and Schützenberger product

Expansions , Free Inverse Semigroups , and Schiitzenberger Product

In this paper we shall present a new constructron of the free inverse monoid on a set A’. Contrary to the prevrous constructions of 19, 111, our construction is symmetric and originates from classrcal ideas of language theory. The mgredlents of this construction are the free group on X and the relatron that associates to a word II’ of the free monoid on X, the set of all pairs (u, v) such that ...

Expansions of Inverse Semigroups

We construct the freest idempotent-pure expansion of an inverse semigroup, generalizing an expansion of Margolis and Meakin for the group case. We also generalize the Birget-Rhodes prefix expansion to inverse semigroups with an application to partial actions of inverse semigroups. In the process of generalizing the latter expansion, we are led to a new class of idempotent-pure homomorphisms whi...

Amalgams of Free Inverse Semigroups

We study inverse semigroup amalgams of the form S U T where S and T are free inverse semigroups and U is an arbitrary nitely generated inverse subsemigroup of S and T. We make use of recent work of Bennett to show that the word problem is decidable for any such amalgam. This is in contrast to the general situation for semigroup amalgams, where recent work of Birget, Margolis and Meakin shows th...

GrÖbner-shirshov Bases for Free Inverse Semigroups

A new construction for free inverse semigroups was obtained by Poliakova and Schein in 2005. Based on their result, we find Gröbner-Shirshov bases for free inverse semigroups with respect to the deg-lex order of words. In particular, we give the (unique and shortest) normal forms in the classes of equivalent words of a free inverse semigroup together with the Gröbner-Shirshov algorithm to trans...

Semidirect Product Decompositions of Ordered Groupoids and Inverse Semigroups