Symmetric inverse semigroup
- Symmetric inverse semigroup
In modern algebra, the set of all partial one-one transformations on a set "X" forms an inverse semigroup, called the symmetric inverse semigroup (or monoid) on "X". In general is not commutative. More details are available in the discussion on the origins of the inverse semigroup.
Finite symmetric inverse semigroups
When "X" is a finite set {1, ..., "n"}, the inverse semigroup of one-one partial transformations is denoted by "C""n" and its elements are called charts [Lipscomb 1997, p. 1] . The notion of chart generalizes the notion of permutation.
Notes
References
S. Lipscomb, "Symmetric Inverse Semigroups", AMS Mathematical Surveys and Monographs (1997), ISBN 0821806270.
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