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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Characterizations of linear congruences on a free monoid


Authors: Alessandra Cherubini and Mario Petrich
Journal: Proc. Amer. Math. Soc. 119 (1993), 719-726
MSC: Primary 20M05
DOI: https://doi.org/10.1090/S0002-9939-1993-1176067-9
MathSciNet review: 1176067
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Abstract: Linear congruences on a free monoid $ {X^{\ast}}$ coincide with the congruences on $ {X^{\ast}}$ induced by nontrivial homomorphisms into the additive group of integers. For a finite $ X$, we characterize abstractly several classes of linear congruences on $ {X^{\ast}}$, in particular, $ \pi $-linear congruences, called $ p$-linear and determined by Reis, $ \xi $-linear congruences, introduced by Petrich and Thierrin, and general linear congruences, introduced by the authors. These characterizations include descriptions involving maximality as prefix congruences.


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DOI: https://doi.org/10.1090/S0002-9939-1993-1176067-9
Keywords: Linear congruence, prefix congruence, congruence lattice, free monoid, shuffle product
Article copyright: © Copyright 1993 American Mathematical Society