ℋ-Cohesive Orders Associated with Inverse Transversals
T. S. Blyth, M. H. Almeida Santos · Communications in Algebra · 2012
On a regular semigroup S a compatible order ≤is defined to be ℋ-cohesive if elements that are comparable under ≤are ℋ-equivalent. In the case where S admits an inverse transversal a complete description of the ℋ-cohesive orders on S is obtained. When S is locally inverse the semilattices of ℋ-cohesive orders and amenable orders are isomorphic, and coincide if and only if S is completely simple.