Аннотация:
In this work we consider monoids as algebras with an associative binary operation and the nullary operation that fixes the identity element. We found an example of two varieties of monoids with finite subvariety lattices such that their join covers one of them and has a continuum cardinality subvariety lattice that violates the ascending chain condition and the descending chain condition.
The work is supported by the Ministry of Education and Science of the Russian Federation (project 1.6018.2017/8.9) and by Russian Foundation for Basic Research (grant 17-01-00551).
Поступила13 февраля 2019 г., опубликована 5 августа 2019 г.
Образец цитирования:
S. V. Gusev, “On the ascending and descending chain conditions in the lattice of monoid varieties”, Сиб. электрон. матем. изв., 16 (2019), 983–997
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\by S.~V.~Gusev
\paper On the ascending and descending chain conditions in the lattice of monoid varieties
\jour Сиб. электрон. матем. изв.
\yr 2019
\vol 16
\pages 983--997
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\crossref{https://doi.org/10.33048/semi.2019.16.067}
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https://www.mathnet.ru/rus/semr1109
https://www.mathnet.ru/rus/semr/v16/p983
Эта публикация цитируется в следующих 6 статьяx:
João Araújo, João Pedro Araújo, Peter J. Cameron, Edmond W.H. Lee, Jorge Raminhos, “A survey on varieties generated by small semigroups and a companion website”, Journal of Algebra, 635 (2023), 698
Edmond W. H. Lee, Frontiers in Mathematics, Advances in the Theory of Varieties of Semigroups, 2023, 1
Sergey V. Gusev, Edmond W. H. Lee, Boris M. Vernikov, “The lattice of varieties of monoids”, Jpn. J. Math., 17:2 (2022), 117
S. V. Gusev, B. M. Vernikov, “Two weaker variants of congruence permutability for monoid varieties”, Semigr. Forum, 103:1 (2021), 106–152
S. V. Gusev, E. W. H. Lee, “Varieties of monoids with complex lattices of subvarieties”, Bull. London Math. Soc., 52:4 (2020), 762–775
С. В. Гусев, “Стандартные элементы решётки многообразий моноидов”, Алгебра и логика, 59:6 (2020), 615–626; S. V. Gusev, “Standard elements of the lattice of monoid varieties”, Algebra and Logic, 59:6 (2021), 415–422
Цитирование в формате AMSBIB
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