On the Lattice of Subvarieties of the Wreath Product of the Variety of Semilattices and the Variety of Semigroups with Zero Multiplication


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Abstract

It is known that the monoid wreath product of any two semigroup varieties that are atoms in the lattice of all semigroup varieties may have a finite as well as an infinite lattice of subvarieties. If this lattice is finite, then as a rule it has at most eleven elements. This was proved in a paper of the author in 2007. The exclusion is the monoid wreath product Sl w N2 of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice L(Sl w N2) of subvarieties of Sl w N2 is still unknown. In our paper, we show that the lattice L(Sl w N2) contains no less than 33 elements. In addition, we give some exponential upper bound of the cardinality of this lattice.

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A. V. Tishchenko

Financial University under the Government of the Russian Federation

Author for correspondence.
Email: alextish@bk.ru
Russian Federation, Moscow

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