ACTA issues

On lattice isomorphisms of orthodox semigroups

Simon M. Goberstein

Acta Sci. Math. (Szeged) 87:3-4(2021), 367-379

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.

DOI: 10.14232/actasm-020-558-7

AMS Subject Classification (1991): 20M15, 20M18, 20M19; 08A30

Keyword(s): torsion-free semigroups, orthodox semigroups, monogenic orthodox semigroups, inverse semigroups, monogenic inverse semigroups, lattice isomorphisms of semigroups, lattice determined semigroups, lattice closed classes of semigroups

received 27.10.2020, revised 4.8.2021, accepted 13.8.2021. (Registered under 58/2020.)