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2015•Unpublished venueRequires access

Every m-permutable variety satisfies the congruence identity αβh = αγh

Paolo Lipparini

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Abstract

Abstract. It is known that m-permutable varieties satisfy non-trivial lattice 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 lattice identity αβh = αγh. By the way, in Section 2, we get a new condition equivalent to m-permutability (Proposition 2.4). 1.

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What this paper is about

Abstract. It is known that m-permutable varieties satisfy non-trivial lattice 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 lattice identity αβh = αγh. By the way, in Section 2, we get a new condition equivalent to m-permutability (Proposition 2.4). 1.

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Available abstract

Abstract. It is known that m-permutable varieties satisfy non-trivial lattice 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 lattice identity αβh = αγh. By the way, in Section 2, we get a new condition equivalent to m-permutability (Proposition 2.4). 1.

Key concepts: Permutable prime, Congruence (geometry), Mathematics, Variety (cybernetics), Identity (music), Pure mathematics, Statistics, Geometry

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