It is known that congruence lattices of algebras in $ m$-permutable varieties satisfy non-trivial identities; however, the identities discovered so far are rather artificial and seem to have little intrinsic interest. We show here that every $ m$-permutable variety satisfies the well-known and well-studied congruence identity $ \alpha \beta_h= \alpha \gamma_h$. We also get a new condition equivalent to $ m$-permutability.
Lipparini, P. (2008). Every m-permutable variety satisfies the congruence identity $alpha beta_h= alpha gamma_h$. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 136, 1137-1144 [10.1090/S0002-9939-07-09337-9].
Every m-permutable variety satisfies the congruence identity $alpha beta_h= alpha gamma_h$
LIPPARINI, PAOLO
2008-01-01
Abstract
It is known that congruence lattices of algebras in $ m$-permutable varieties satisfy non-trivial identities; however, the identities discovered so far are rather artificial and seem to have little intrinsic interest. We show here that every $ m$-permutable variety satisfies the well-known and well-studied congruence identity $ \alpha \beta_h= \alpha \gamma_h$. We also get a new condition equivalent to $ m$-permutability.File in questo prodotto:
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