Amalgamation for inverse and generalized inverse semigroups

Amalgamation for Inverse and Generalized Inverse Semigroups

For any amalgam (S, T; U) of inverse semigroups, it is shown that the natural partial order on S *u T, the (inverse semigroup) free product of S and T amalgamating U, has a simple form onSUT. In particular, it follows that the semilattice of 5 *u T is a bundled semilattice of the corresponding semilattice amalgam (E(S), E(T); E(U)); taken jointly with a result of Teruo Imaoka, this gives that t...

Anisimov's Theorem for inverse semigroups

The idempotent problem of a finitely generated inverse semi-group is the formal language of all words over the generators representing idempotent elements. This note proves that a finitely generated inverse semigroup with regular idempotent problem is necessarily finite. This answers a question of Gilbert and Noonan Heale, and establishes a gen-eralisation to inverse semigroups of Anisimov's Th...

Brandt extensions and primitive topologically periodic inverse topological semigroups

In this paper we find sufficient conditions on primitive inverse topological semigroup S under which: the inversion inv : (H(S)) (H(S)) is continuous; we show that every topologically periodic countable compact primitive inverse topological semigroups with closed H-classes is topologically isomorphic to an orthogonal sum P i2= Bi (Gi) of topological Brandt extensions Bi (Gi) of countably compac...

Primer on Inverse Semigroups

Semigroups of inverse quotients

We examine, in a general setting, a notion of inverse semigroup of left quotients, which we call left I-quotients. This concept has appeared, and has been used, as far back as Clifford’s seminal work describing bisimple inverse monoids in terms of their right unit subsemigroups. As a consequence of our approach, we find a straightforward way of extending Clifford’s work to bisimple inverse semi...