Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

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



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
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 ${\tau ^{ - 1}}(0) = 1$.

References [Enhancements On Off] (What's this?)

  • Samuel Eilenberg, Automata, languages, and machines. Vol. A, Academic Press [A subsidiary of Harcourt Brace Jovanovich, Publishers], New York, 1974. Pure and Applied Mathematics, Vol. 58. MR 0530382
  • Y. Q. Guo, H. J. Shyr and G. Thierrin, $f$-disjunctive languages, Internat. J. Comput. Math. 18 (1986), 219-237.
  • Leonard H. Haines, On free monoids partially ordered by embedding, J. Combinatorial Theory 6 (1969), 94–98. MR 240016
  • J. L. Kelley and Isaac Namioka, Linear topological spaces, The University Series in Higher Mathematics, D. Van Nostrand Co., Inc., Princeton, N.J., 1963. With the collaboration of W. F. Donoghue, Jr., Kenneth R. Lucas, B. J. Pettis, Ebbe Thue Poulsen, G. Baley Price, Wendy Robertson, W. R. Scott, Kennan T. Smith. MR 0166578
  • Gérard Lallement, Semigroups and combinatorial applications, John Wiley & Sons, New York-Chichester-Brisbane, 1979. Pure and Applied Mathematics; A Wiley-Interscience Publication. MR 530552
  • C. M. Reis, A note on $F$-disjunctive languages, Semigroup Forum 36 (1987), no. 2, 159–165. MR 911052, DOI
  • H. J. Shyr and G. Thierrin, Hypercodes, Information and Control 24 (1974), 45–54. MR 345712

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 20M05

Retrieve articles in all journals with MSC: 20M05

Additional Information

Keywords: Infix congruences, free monoid, commutative maximal infix congruences
Article copyright: © Copyright 1989 American Mathematical Society