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 Fundam. Prikl. Mat., 2016, Volume 21, Issue 3, Pages 107–120 (Mi fpm1736)

Pseudocomplements in the lattice of subvarieties of a variety of multiplicatively idempotent semirings

E. M. Vechtomov, A. A. Petrov

Vyatka State University

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

 Funding Agency Grant Number Ministry of Education and Science of the Russian Federation 1.1375.2014/Ê

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English version:
Journal of Mathematical Sciences (New York), 2019, 237:3, 410–419

UDC: 512.558

Citation: E. M. Vechtomov, A. A. Petrov, “Pseudocomplements in the lattice of subvarieties of a variety of multiplicatively idempotent semirings”, Fundam. Prikl. Mat., 21:3 (2016), 107–120; J. Math. Sci., 237:3 (2019), 410–419

Citation in format AMSBIB
\Bibitem{VecPet16} \by E.~M.~Vechtomov, A.~A.~Petrov \paper Pseudocomplements in the lattice of subvarieties of a~variety of multiplicatively idempotent semirings \jour Fundam. Prikl. Mat. \yr 2016 \vol 21 \issue 3 \pages 107--120 \mathnet{http://mi.mathnet.ru/fpm1736} \transl \jour J. Math. Sci. \yr 2019 \vol 237 \issue 3 \pages 410--419 \crossref{https://doi.org/10.1007/s10958-019-04166-4}