2016/01/29 by Nouf AlYamani, AlYamani, Nouf, N. D. Gilbert +1
Computer Science · Mathematics · #semigroups and automata theory #Advanced Operator Algebra Research #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1601.08194
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 ≃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.