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

Аннотация

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.