Inverse Semigroups with Isomorphic Bundles ofi-Correspondences

✍ Scribed by Simon M. Goberstein

• Publisher: Elsevier Science
• Year: 1996
• Tongue: English
• Weight: 222 KB
• Volume: 184
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1996.0254

✦ Synopsis

An i-correspondence of an inverse semigroup S is any inverse subsemigroup of S = S, and the set of all i-correspondences of S, with the operations of composition and involution and the relation of set-theoretic inclusion, forms the bundle of Ž . i-correspondences of S, denoted by Ci S . For inverse semigroups S and T, any Ž . Ž . isomorphism of Ci S onto Ci T is called a Ci-isomorphism of S upon T. An inverse semigroup is said to be Ci-determined if it is isomorphic to any inverse semigroup Ci-isomorphic to it. In this paper we develop a method for studying Ž . Ci-isomorphisms of arbitrary nonperiodic inverse semigroups and, using it, prove that any fundamental inverse semigroup is Ci-determined. Furthermore, we establish a connection between Ci-isomorphisms of inverse semigroups and their C-isow morphisms and deduce as a corollary the main result of S. M. Goberstein, Ž .

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