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Transactions of the American Mathematical Society

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Infix congruences on a free monoid


Author: C. M. Reis
Journal: Trans. Amer. Math. Soc. 311 (1989), 727-737
MSC: Primary 20M05
MathSciNet review: 978373
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Abstract: A congruence $ \rho $ on a free monoid $ {X^{\ast}}$ is said to be infix if each class $ C$ of $ \rho $ satisfies $ u \in C$ and $ xuy \in C$ imply $ xy = 1$.

The main purpose of this paper is a characterization of commutative maximal infix congruences. These turn out to be congruences induced by homomorphisms $ \tau $ from $ {X^{\ast}}$ to $ {{\mathbf{N}}^0}$, the monoid of nonnegative integers under addition, with $ {\tau ^{ - 1}}(0) = 1$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1989-0978373-0
Keywords: Infix congruences, free monoid, commutative maximal infix congruences
Article copyright: © Copyright 1989 American Mathematical Society