On left quasi-ample semigroups with ΠL1-embeddable band of idempotents - Billhardt B. (2017)
© 2017 Taylor & Francis. Let ΠL 1 denote a direct power of L 1 , the two-element left zero semigroup with identity adjoined. A semigroup S is called left quasi-ample if for each a∈S there exists a unique idempotent a + ∈S such that xa = ya ⇔ xa + = ya + for all x, y∈S 1 and the left ample condition e 2 = e ⇒ (ae) + a = ae holds. Generalizing a recent result in [3], we prove that the semigroups in the title are embeddable into certain transformation semigroups. Our embedding provides an easy way to construct (finite) proper covers for (finite) such semigroups. Moreover, we show that each proper such semigroup is embeddable into a semidirect product of a ΠL 1 -embeddable band by a right cancellative monoid, giving a partial answer to a question raised in [1].