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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 N 2 of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice L(Sl w N 2) of subvarieties of Sl w N 2 is still unknown. In our paper, we show that the lattice L(Sl w N 2) contains no less than 33 elements. In addition, we give some exponential upper bound of the cardinality of this lattice.

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Authors and Affiliations

  1. Financial University under the Government of the Russian Federation, Moscow, Russia

    A. V. Tishchenko

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  1. A. V. Tishchenko
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Correspondence to A. V. Tishchenko.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 19, No. 6, pp. 191–212, 2014.

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Tishchenko, A.V. On the Lattice of Subvarieties of the Wreath Product of the Variety of Semilattices and the Variety of Semigroups with Zero Multiplication. J Math Sci 221, 436–451 (2017). https://doi.org/10.1007/s10958-017-3236-4

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