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Journal of Mathematical Sciences

, Volume 237, Issue 3, pp 410–419 | Cite as

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

  • E. M. VechtomovEmail author
  • A. A. Petrov
Article
  • 5 Downloads

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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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Vyatka State UniversityVyatkaRussia

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