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Upper-modular and related elements of the lattice of commutative semigroup varieties

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Abstract

We completely determine upper-modular, codistributive and costandard elements in the lattice of all commutative semigroup varieties. In particular, we prove that the properties of being upper-modular and codistributive elements in the mentioned lattice are equivalent. Moreover, in the nil-case the properties of being elements of all three types turn out to be equivalent.

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Acknowledgements

The author thanks the anonymous referee for several constructive remarks that helped to improve the manuscript. Supported by the Ministry of Education and Science of the Russian Federation (Project 2248) and by Russian Foundation for Basic Research (Grant 14-01-00524).

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Authors and Affiliations

  1. Institute of Mathematics and Computer Science, Ural Federal University, Lenina 51, Ekaterinburg, Russia, 620000

    B. M. Vernikov

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  1. B. M. Vernikov
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Correspondence to B. M. Vernikov.

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Communicated by Mikhail Volkov.

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Vernikov, B.M. Upper-modular and related elements of the lattice of commutative semigroup varieties. Semigroup Forum 94, 696–711 (2017). https://doi.org/10.1007/s00233-016-9843-4

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  • DOI: https://doi.org/10.1007/s00233-016-9843-4

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