Amalgamating inverse semigroups over ample semigroups

TL;DR

This paper investigates conditions under which semigroup amalgams involving inverse semigroups can be embedded, providing new non-embeddability criteria and sufficient conditions for weak embeddability.

Contribution

It introduces novel non-embeddability conditions and criteria for weak embeddability of inverse semigroup amalgams, expanding understanding of their structural properties.

Findings

Established non-embeddability conditions for certain inverse semigroup amalgams.

Identified sufficient conditions for the inverse hulls to be isomorphic.

Provided criteria for weak embeddability of the amalgams.

Abstract

A semigroup amalgam (S; T1, T2) is known to be non-embeddable if T1 and T2 are both groups (completely regular semigroups, Clifford semigroups) but S is not such. We prove some non-embeddability conditions for semigroup amalgams (S; T1, T2) in which T1 and T2 are inverse semigroups but S is not such. We also introduce some sufficient conditions that make the inverse hulls of the copies of S in T1 and T2 isomorphic; making, in turn, the amalgam (S; T1, T2) weakly embeddable.