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presentation of inverse monoids and inverse semigroups
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(Definition)
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Let
be the free monoid with involution on , and
be a binary relation between words. We denote by
[resp.
] the equivalence relation [resp. congruence] generated by .
A presentation (for an inverse monoid) is a couple . We use this couple of objects to define an inverse monoid
. Let be the Wagner congruence on , we define the inverse monoid
presented by as
In the previous dicussion, if we replace everywhere
with
we obtain a presentation (for an inverse semigroup) and an inverse semigroup
presented by .
A trivial but important example is the Free Inverse Monoid [resp. Free Inverse Semigroup] on , that is usually denoted by
[resp.
] and is defined by
- 1
- N. Petrich, Inverse Semigroups, Wiley, New York, 1984.
- 2
- J.B. Stephen, Presentation of inverse monoids, J. Pure Appl. Algebra 63 (1990) 81-112.
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"presentation of inverse monoids and inverse semigroups" is owned by Mazzu.
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(view preamble)
| Other names: |
presentation, generators and relators |
| Keywords: |
Inverse Semigroups, Word Problem, Isomorphism Problem |
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Cross-references: free inverse semigroup, free inverse monoid, inverse semigroup, Wagner congruence, objects, monoid, inverse, congruence generated by, equivalence relation, words, binary relation, free monoid with involution
There are 8 references to this entry.
This is version 7 of presentation of inverse monoids and inverse semigroups, born on 2006-08-21, modified 2006-08-24.
Object id is 8271, canonical name is PresentationOfInverseMonoidsAndInverseSemigroups.
Accessed 1359 times total.
Classification:
| AMS MSC: | 20M18 (Group theory and generalizations :: Semigroups :: Inverse semigroups) | | | 20M05 (Group theory and generalizations :: Semigroups :: Free semigroups, generators and relations, word problems) |
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Pending Errata and Addenda
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