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

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.