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- Title
On the Lattice of Subvarieties of the Wreath Product of the Variety of Semilattices and the Variety of Semigroups with Zero Multiplication.
- Authors
Tishchenko, A.
- 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 of the variety of semilattices and the variety of semigroups with zero multiplication. The number of elements of the lattice L( Sl w N ) of subvarieties of Sl w N is still unknown. In our paper, we show that the lattice L( Sl w N ) contains no less than 33 elements. In addition, we give some exponential upper bound of the cardinality of this lattice.
- Subjects
WREATH products (Group theory); SEMILATTICES; VARIETIES (Universal algebra); SEMIGROUPS (Algebra); MONOIDS
- Publication
Journal of Mathematical Sciences, 2017, Vol 221, Issue 3, p436
- ISSN
1072-3374
- Publication type
Article
- DOI
10.1007/s10958-017-3236-4