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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Infix congruences on a free monoid
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by C. M. Reis PDF
Trans. Amer. Math. Soc. 311 (1989), 727-737 Request permission


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
  • © Copyright 1989 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 311 (1989), 727-737
  • MSC: Primary 20M05
  • DOI:
  • MathSciNet review: 978373