# An elegant 3-basis for inverse semigroups - Mathematics > Group Theory

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Abstract: It is well known that in every inverse semigroup the binary operation and theunary operation of inversion satisfy the following three identities: \quadx=xx-x \qquad \quad xx-y-y=y-yxx- \qquad \quad xyz=xyz-. Thegoal of this note is to prove the converse, that is, we prove that an algebraof type $<2,1>$ satisfying these three identities is an inverse semigroup andthe unary operation coincides with the usual inversion on such semigroups.

Autor: Joao Araujo, Michael Kinyon

Fuente: https://arxiv.org/

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