Sib. Èlektron. Mat. Izv., 2019, Volume 16, Pages 983–997
Mathematical logic, algebra and number theory
On the ascending and descending chain conditions in the lattice of monoid varieties
S. V. Gusev
Ural Federal University, Institute of Natural Sciences and Mathematics 51, Lenina ave., Ekaterinburg, 620000, Russia
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.
monoid, variety, lattice of varieties, ascending chain condition, descending chain condition.
PDF file (187 kB)
MSC: 20M07, 08B15
Received February 13, 2019, published August 5, 2019
S. V. Gusev, “On the ascending and descending chain conditions in the lattice of monoid varieties”, Sib. Èlektron. Mat. Izv., 16 (2019), 983–997
Citation in format AMSBIB
\paper On the ascending and descending chain conditions in the lattice of monoid varieties
\jour Sib. \`Elektron. Mat. Izv.
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