presentation of inverse monoids and inverse semigroups
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
References
- 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.
Title | presentation of inverse monoids and inverse semigroups |
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Canonical name | PresentationOfInverseMonoidsAndInverseSemigroups |
Date of creation | 2013-03-22 16:11:01 |
Last modified on | 2013-03-22 16:11:01 |
Owner | Mazzu (14365) |
Last modified by | Mazzu (14365) |
Numerical id | 10 |
Author | Mazzu (14365) |
Entry type | Definition |
Classification | msc 20M05 |
Classification | msc 20M18 |
Synonym | presentation |
Synonym | generators and relators |