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Representation of inverse monoids by partial automorphisms
It is shown that any inverse semigroup of endomorphisms of an object in a properly (E, M)-structured category admitting intersections may be embedded in an inverse monoid of partial automorphisms between retracts of that object. It follows that every inverse monoid is isomorphic with an inverse monoid of all partial automorphisms between [non-trivial] retracts of some object of any [almost] algebraically universal and properly (E, M)-structured category with intersections; in particular, of an [almost] algebraically universal and finitely complete category with arbitrary intersections. Several examples are given.
History
Publication title
Semigroup ForumVolume
61Pagination
357-362ISSN
0037-1912Department/School
School of Natural SciencesPublisher
Springer VerlagPlace of publication
New YorkRepository Status
- Restricted