Geodesic
Pseudocomplements in the lattice of subvarieties of a variety of multiplicatively idempotent semirings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 107-120 
E. M. Vechtomov; A. A. Petrov. Pseudocomplements in the lattice of subvarieties of a variety of multiplicatively idempotent semirings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 21 (2016) no. 3, pp. 107-120. http://geodesic.mathdoc.fr/item/FPM_2016_21_3_a5/
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     title = {Pseudocomplements in the lattice of subvarieties of a~variety of multiplicatively idempotent semirings},
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Voir la notice de l'article provenant de la source Math-Net.Ru

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.

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