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Proceedings of the American Mathematical Society

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

 

 

A ring with arithmetical congruence lattice not preserved by any Pixley function


Author: Ivan Korec
Journal: Proc. Amer. Math. Soc. 82 (1981), 23-27
MSC: Primary 16A99; Secondary 08A30
DOI: https://doi.org/10.1090/S0002-9939-1981-0603594-4
MathSciNet review: 603594
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Abstract: A ring $ (A; + , \cdot )$ is constructed such that the congruence lattice $ {L_A}$ of the ring $ (A; + , \cdot )$ is distributive, the elements of $ {L_A}$ are pairwise permutable and there is no $ {L_A}$-compatible function $ p$ on $ A$ such that

$\displaystyle p(a,b,b) = p(a,b,a) = p(b,b,a) = a\quad {\text{for}}\;{\text{all}}\;a,b \in A.$

(1)

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DOI: https://doi.org/10.1090/S0002-9939-1981-0603594-4
Article copyright: © Copyright 1981 American Mathematical Society