Pseudocomplements in the Lattice of Subvarieties of a Variety of Multiplicatively Idempotent Semirings
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The lattice L(𝔐) of all subvarieties of the variety 𝔐 of multiplicatively idempotent semirings is studied. Some relations have been obtained. It is proved that L(𝔐) is a pseudocomplemented lattice. Pseudocomplements in the lattice L(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(𝔐) is infinite and nonmodular.
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