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- W2257029120 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 ${mathscr J}$-relation. The corresponding equivalence relation $simeq_N$ 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." @default.
- W2257029120 created "2016-06-24" @default.
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- W2257029120 date "2016-01-29" @default.
- W2257029120 modified "2023-10-16" @default.
- W2257029120 title "Ordered groupoid quotients and congruences on inverse semigroups" @default.
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- W2257029120 doi "https://doi.org/10.48550/arxiv.1601.08194" @default.
- W2257029120 hasPublicationYear "2016" @default.
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