Email this article Pseudocomplements in the Lattice of Subvarieties of a Variety of Multiplicatively Idempotent Semirings
- Authors: Vechtomov E.M.1, Petrov A.A.1
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Affiliations:
- Vyatka State University
- Issue: Vol 237, No 3 (2019)
- Pages: 410-419
- Section: Article
- URL: https://ogarev-online.ru/1072-3374/article/view/242355
- DOI: https://doi.org/10.1007/s10958-019-04166-4
- ID: 242355
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Abstract
The lattice L(????) of all subvarieties of the variety ???? of multiplicatively idempotent semirings is studied. Some relations have been obtained. It is proved that L(????) is a pseudocomplemented lattice. Pseudocomplements in the lattice L(????) 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(????) is infinite and nonmodular.
About the authors
E. M. Vechtomov
Vyatka State University
Author for correspondence.
Email: vecht@mail.ru
Russian Federation, Vyatka
A. A. Petrov
Vyatka State University
Email: vecht@mail.ru
Russian Federation, Vyatka
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