Inverse semigroups on graphs |
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Authors: | C J Ash T E Hall |
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Institution: | 1. Monash University, 3168, Clayton, Victoria, Australia
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Abstract: | For each directed] graph we construct an inverse semigroup. Our main application is a simple proof of the characterization of partially ordered sets ofJ-classes of finite semigroups, and some generalizations; our proof avoids using the inductive construction of the previous method by one of the authors 4]. For a connected graph in which each vertex has index at least two, our construction gives a congruence free inverse semigroup. In the final section we describe how a slight modification bf the construction yields the polycyclic monoids. |
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