Characterizations of linear congruences on a free monoid
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- by Alessandra Cherubini and Mario Petrich PDF
- Proc. Amer. Math. Soc. 119 (1993), 719-726 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- 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