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Covering elements in the lattice op varieties of algebras

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Abstract

Let variety μ be given by the balanced identities of signature Ω not containing unary operations. Then, in the lattice of subvarieties of variety μ, any element different from μ has an element covering it. In particular, variety μ might be the varieties of semigroups, groupoids, n-associatives, etc. It is also proven that, in the lattice of varieties of semigroups, there exists an element having a continuum of covering elements.

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Literature cited

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Authors and Affiliations

  1. Ural Polytechnic Institute, USSR

    A. N. Trakhtman

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  1. A. N. Trakhtman
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Translated from Matematicheskie Zametki, Vol. 15, No. 2, pp. 307–312, February, 1974.

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Trakhtman, A.N. Covering elements in the lattice op varieties of algebras. Mathematical Notes of the Academy of Sciences of the USSR 15, 174–177 (1974). https://doi.org/10.1007/BF02102402

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  • DOI: https://doi.org/10.1007/BF02102402

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