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

Korec, Ivan

doi:10.1090/S0002-9939-1981-0603594-4

A ring with arithmetical congruence lattice not preserved by any Pixley function
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Proc. Amer. Math. Soc. 82 (1981), 23-27 Request permission

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 \[ p(a,b,b) = p(a,b,a) = p(b,b,a) = a\quad {\text {for}}\;{\text {all}}\;a,b \in A.\] (1)

References

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Combinatorial identities

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