Ordered groupoid quotients and congruences on inverse semigroups

Nouf Abduljabar Alyamani, Nicholas David Gilbert

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Abstract

We introduce a preorder on an inverse semigroup S associated to any normal inverse subsemigroup N, that lies between the natural partial order and Green’s JJ –relation. The corresponding equivalence relation ≃N≃N is not necessarily a congruence on S, but the quotient set does inherit a natural ordered groupoid structure. We show that this construction permits the factorisation of any inverse semigroup homomorphism into a composition of a quotient map and a star-injective functor, and that this decomposition implies a classification of congruences on S. We give an application to the congruence and certain normal inverse subsemigroups associate to an inverse monoid presentation.
Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalSemigroup Forum
Early online date2 Aug 2017
DOIs
Publication statusE-pub ahead of print - 2 Aug 2017

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