Structure mappings, coextensions and regular four-spiral semigroups

Abstract

The structure mapping approach to regular semigroups developed by K. S. S. Nambooripad and J. Meakin is used to describe the K \mathcal {K} -coextensions of the fundamental four-sprial semigroup and hence to describe the structure of all regular semigroups whose idempotents form a four-spiral biordered set. Isomorphisms between regular four-spiral semigroups are studied. The notion of structural uniformity of a regular semigroup is defined and exploited.