E-separated semigroups
Тарас Онуфриевич Банах · Visnyk Lvivskogo Universytetu Seriya Mekhaniko-Matematychna · 2021
A semigroup is called E-separated if for any distinct idempotents x , y ∈ X there exists a homomorphism h : X → Y to a semilattice Y such that h ( x ) ≠ h ( y ) . Developing results of Putcha and Weissglass, we characterize E-separated semigroups via certain commutativity properties of idempotents of X . Also we characterize E-separated semigroups in the class of π -regular E-semigroups.