On lattice ordered periodic semigroups
Thérèse Merlier · Czechoslovak Mathematical Journal · 1993
As in our previous papers [3], [4], [5], by a lattice ordered semigroup, we mean a semigroup S on which we can define an order relation -^ such that -(S, ^) is a distributive lattice; A and V are the least upper bound and the greatest lower bound.-Va V6 Vc a(b A c) = a6 A ac and (b A c)a = 6a A ca -VaV6Vc a(6Vc) = ab V ac and (6 V c)a = 6a V ca.The purpose of this note is to give some algebraic properties of lattice ordered periodic semigroups and particularly in the finite case. 1. LATTICE ORDERED NILSEMIGROUPS.LATTICE ORDERED PERIODIC SEMIGROUPS a 2 Vб a, Vб If we put a 2 6 = a\, ba 2 = e, we obtain the following multiplication table, which is effectively the one of a semigroup e