Inverse Semigroups with Isomorphic Bundles ofi-Correspondences Original Research Article

Ani-correspondence of an inverse semigroupSis any inverse subsemigroup ofS×S, and the set of alli-correspondences ofS, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle ofi-correspondences ofS, denoted byCi(S). For inverse semigroupsSandT, any isomorphism ofCi(S) ontoCi(T) is called aCi-isomorphism ofSuponT. An inverse semigroup is said to beCi-determined if it is isomorphic to any inverse semigroupCi-isomorphic to it. In this paper we develop a method for studyingCi-isomorphisms of arbitrary (nonperiodic) inverse semigroups and, using it, prove that any fundamental inverse semigroup isCi-determined. Furthermore, we establish a connection betweenCi-isomorphisms of inverse semigroups and theirC-isomorphisms and deduce as a corollary the main result of [S. M. Goberstein,J. Algebra125(1989), 474–488].