On lattice isomorphisms of orthodox semigroups

TL;DR

This paper proves that the class of orthodox semigroups with all nonidempotent elements of infinite order is lattice closed, enhancing understanding of their structural properties through lattice isomorphisms.

Contribution

It establishes that orthodox semigroups with infinite order nonidempotents form a lattice closed class, a novel structural insight in semigroup theory.

Findings

The class of all orthodox semigroups with infinite order nonidempotents is lattice closed.

Lattice isomorphisms preserve the structure of these semigroups.

The result advances the classification of semigroups based on lattice properties.

Abstract

Two semigroups are lattice isomorphic if the lattices of their subsemigroups are isomorphic, and a class of semigroups is lattice closed if it contains every semigroup which is lattice isomorphic to some semigroup from that class. An orthodox semigroup is a regular semigroup whose idempotents form a subsemigroup. We prove that the class of all orthodox semigroups in which every nonidempotent element has infinite order is lattice closed.