Inverse semigroups whose full inverse subsemigroups form a chain

Permutative Semigroups Whose Congruences Form a Chain ∗

Semigroups whose congruences form a chain are often termed ∆-semigroups. The commutative ∆-semigroups were determined by Schein and by Tamura. A natural generalization of commutativity is permutativity: a semigroup is permutative if it satisfies a non-identity permutational identity. We completely determine the permutative ∆-semigroups. It turns out that there are only six noncommutative exampl...

Homomorphisms and congruences on regular semigroups with associate inverse subsemigroups

An associate inverse subsemigroup of a regular semigroup S is a subsemigroup T of S containing a least associate x∗ of each x ∈ S, in relation to the natural partial order ≤S in S. In [1] the authors describe the structure of regular semigroups with an associate inverse subsemigroup, satisfying two natural conditions. In this paper we describe all ∗-congruences on such class of semigroups.

Inverse subsemigroups of the monogenic free inverse semigroup

It is shown that every finitely generated inverse subsemigroup (submonoid) of the monogenic free inverse semigroup (monoid) is finitely presented. As a consequence, the homomorphism and the isomorphism problems for the monogenic free inverse semigroup (monoid) are proved to be decidable.

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...

Primer on Inverse Semigroups