A Biordered Set Representation of Regular Semigroups.

In this paper, for an arbitrary regular biordered setE, by using biorder-isomorphisms between the ?-ideals ofE, we construct a fundamental regular semigroupW_E called NH-semigroup ofE, whose idempotent biordered set is isomorphic toE. We prove further thatW_E can be used to give a new representation of general regular semigroups in the sense that, for any regular semigroupSwith the idempotent biordered set isomorphic toE, there exists a homomorphism fromStoW_E whose kernel is the greatest idempotent-separating congruence onSand the image is a full symmetric subsemigroup ofW_E. Moreover, whenEis a biordered set of a semilatticeE₀,W_E is isomorphic to the Munn-semigroup; and whenEis the biordered set of a bandB,W_E is isomorphic to the Hall-semigroupW_B. [ABSTRACT FROM AUTHOR]