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Proceedings of the American Mathematical Society

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

 

 

When are Rees congruences principal?


Author: C. M. Reis
Journal: Proc. Amer. Math. Soc. 106 (1989), 593-597
MSC: Primary 20M05; Secondary 20M10, 20M12
DOI: https://doi.org/10.1090/S0002-9939-1989-0964460-5
MathSciNet review: 964460
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Abstract: Let $ {\rho _I}$ be the Rees congruence modulo the ideal $ I$ of the free monoid $ {X^*}$. In this short note we give necessary and sufficient conditions, in terms of the partial order induced by division on the complement of $ I$, for $ {\rho _I}$ to be principal. In particular, we prove that if $ I$ is principal, so is $ {\rho _I}$.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0964460-5
Article copyright: © Copyright 1989 American Mathematical Society