Abstract
A semigroup S with a sub-band B is called a good B-quasi-Ehresmann semigroup if it is a B-semiabundant semigroup satisfying the congruence condition such that aB(a*)B(b+)b+ ⊆ B((ab)+)abB((ab)*) for all a, b ∈ S. We show that every good B-quasi-Ehresmann semigroup has a global representation and a standard representation. As a special case, the structure of good quasi-adequate semigroups is described.
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