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Pseudocomplements in the Lattice of Subvarieties of a Variety of Multiplicatively Idempotent Semirings

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Abstract

The lattice L(𝔐) of all subvarieties of the variety 𝔐 of multiplicatively idempotent semirings is studied. Some relations have been obtained. It is proved that L(𝔐) is a pseudocomplemented lattice. Pseudocomplements in the lattice L(𝔐) are described. It is shown that they form a 64-element Boolean lattice with respect to the inclusion. It is established that the lattice L(𝔐) is infinite and nonmodular.

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Authors and Affiliations

  1. Vyatka State University, Vyatka, Russia

    E. M. Vechtomov & A. A. Petrov

Authors
  1. E. M. Vechtomov
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  2. A. A. Petrov
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Correspondence to E. M. Vechtomov.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 21, No. 3, pp. 107–120, 2016.

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Vechtomov, E.M., Petrov, A.A. Pseudocomplements in the Lattice of Subvarieties of a Variety of Multiplicatively Idempotent Semirings. J Math Sci 237, 410–419 (2019). https://doi.org/10.1007/s10958-019-04166-4

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  • DOI: https://doi.org/10.1007/s10958-019-04166-4

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