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Proceedings of the American Mathematical Society

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

 

 

A note on the congruence lattice of a finitely generated algebra


Authors: Ivan Rival and Bill Sands
Journal: Proc. Amer. Math. Soc. 72 (1978), 451-455
MSC: Primary 08A30
MathSciNet review: 509233
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Abstract: Let $ \mathfrak{A}$ be a finitely generated algebra of finite type. If $ \theta $ is a congruence relation of $ \mathfrak{A}$ such that $ \mathfrak{A}/\theta $ is finite then $ \theta $ is compact in the lattice $ {\text{Con}}(\mathfrak{A})$ of all congruence relations of $ \mathfrak{A}$. Moreover, if $ \mathfrak{A}$ is infinite then there is a congruence relation $ \theta $ such that $ \mathfrak{A}/\theta $ is infinite and $ \mathfrak{A}/\theta '$ is finite for every $ \theta ' > \theta $ in $ {\text{Con}}(\mathfrak{A})$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0509233-5
Article copyright: © Copyright 1978 American Mathematical Society