In mathematics, an inverse semigroup S is a semigroup in which every element x in S has a unique inverse y in S in the sense that x = xyx and y = yxy. Inverse semigroups appear in a range of contexts; for example, they can be employed in the study of partial symmetries.
(The convention followed in this article will be that of writing a function on the right of its argument, and composing functions from left to right — a convention often observed in semigroup theory.)
Read more about Inverse Semigroup: Origins, The Basics, The Natural Partial Order, Homomorphisms and Representations of Inverse Semigroups, Congruences On Inverse Semigroups, E-unitary Inverse Semigroups, Free Inverse Semigroups, Connections With Category Theory, Generalisations of Inverse Semigroups
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“The quality of moral behaviour varies in inverse ratio to the number of human beings involved.”
—Aldous Huxley (1894–1963)