Free Strict Inverse Semigroups

✍ Scribed by K. Auinger

• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 685 KB
• Volume: 157
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1993.1088

✦ Synopsis

A strict inverse semigroup can be constructed by means of the partially ordered set (X=S / \mathscr{f}) of its principal ideals, its (\mathscr{f})-classes which are the non-zero parts of Brandt semigroups, and partial homomorphisms between these partial semigroups. The free object in a variety of strict inverse semigroups is described in terms of these parameters. The associated partial order is realized as a set of symmetric and transitive relations on a certain set, and the corresponding Brandt semigroups as well as the partial homomorphisms can be obtained in a canonical way. As an application, a simple solution of the word problem in the free combinatorial strict inverse semigroup is presented. 1993 Academic Press, Inc.