Extensions of semilattices by left type-A semigroups
Bernd Billhardt · Glasgow Mathematical Journal · 1997
On a semigroup S let the relation ℛ*, sometimes denoted by ℛ , be defined by xℛ*y [( sx = tx sy = ty]. A semigroup S is called left type-A, iff the set Es of idempotents of S forms a semilattice under multiplication, each element x of Sis ℛ* related to a (necessarily unique) idempotent x+, and xe = (xe)+x for all x ∈ S, е ∈ Es.