Symmetric inverse semigroup
- Symmetric inverse semigroup
In modern algebra, the set mathcal{I}_X 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 mathcal{I}_X 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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