A monoid is a set with an operation that is associative and has an identity element.

Any finite monoid can be represented as a set of functions from a finite set to itself.

For any natural k, T_k is the monoid of all functions from the set {1,...,k} to itself, where the operation is composition of functions. There are k^k elements in this monoid, and the identity element is the identity function.

A monoid homomorphism is a function f from one monoid M to another monoid N, with the property that f(xy) = f(x)f(y) for any two elements x and y of M.

-- BarrinG - 2012-04-30

Topic revision: r1 - 2012-04-30 - BarrinG
This site is powered by the TWiki collaboration platform Powered by PerlCopyright © 2008-2019 by the contributing authors. All material on this collaboration platform is the property of the contributing authors.
Ideas, requests, problems regarding UMass CS EdLab? Send feedback

mersin escort adana escort izmir escort gaziantep escort