Abstract
Information about a semigroup can often be gleaned from its partial algebra of idempotents. For example, the idempotents of an inverse semigroup form a semilattice. All isomorphisms between principal ideals of a semilattice E form the Munn inverse semigroup T,, which contains the fundamental image of every inverse semigroup whose idempotents form the semilattice E [ll, 123. Thus semilattices give rise to all fundamental inverse semigroups. Successful efforts have been made to generalize the Munn construction to the wider class of regular semigroups [ 1,6-9, 13, 141. Nambooripad achieved this using the concept of a regular biordered set. The biordered set of a semigroup S means simply the partial algebra consisting of the set E = E(S) of idempotents of S with multiplication restricted to
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