Inverse semigroup

In group theory, an inverse semigroup (occasionally called an inversion semigroup^[1]) 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, i.e. a regular semigroup in which every element has a unique inverse. Inverse semigroups appear in a range of contexts; for example, they can be employed in the study of partial symmetries.^[2]

(The convention followed in this article will be that of writing a function on the right of its argument, e.g. x f rather than f(x), and composing functions from left to right—a convention often observed in semigroup theory.)

^ Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics (2nd ed.). CRC Press. p. 1528. ISBN 978-1-4200-3522-3.
^ Lawson 1998

[Weisstein2002-1] Weisstein, Eric W. (2002). CRC Concise Encyclopedia of Mathematics (2nd ed.). CRC Press. p. 1528. ISBN 978-1-4200-3522-3.

[2] Lawson 1998

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