Semilattices of finite arithmetical algebras
Ivan Chajda · Czechoslovak Mathematical Journal · 1995
An algebra A is arithmetical if the congruence lattice Con A is distributive and every two congruences 0, $ G Con A permute, i.e. 0o$ = $o0.It is easy to see that A is arithmetical if and only if the identity (*) 0n($o$)c(0n$)o(en$) holds for every Q,$,$ G Con A, see e.g.[3], [4] (the symbol o denotes relational product).As was shown in [3], an algebra A is arithmetical if and only if it satisfies the Chinese remainder theorem.The famous characterization was given by A. F. Pixley [3] for finite algebras: