Right (left) inverse semigroups

AbstractA semigroup S (with zero) is called a right inverse semigroup if every (nonnull) principal left ideal of S has a unique idempotent generator. A set of equivalent statements that characterize right inverse semigroups S are given. It is shown that (1) a homomorphic image of S is a right inverse semigroup, (2) the regular representation and the Schützenberger representation M of S are faithful, (3) (under suitable hypotheses) the method used by Preston to embed an inverse semigroup T in It can be extended to give a faithful representation of S in Bs, and (4) S0 is a primitive right inverse semigroup if and only if it is a 0-direct union of right Brandt semigroups. Representations of a left inverse semigroup S by one-to-one transformations of S are obtained