Geodesic
On the ascending and descending chain conditions in the lattice of monoid varieties
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 983-997

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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.
Keywords: monoid, variety, lattice of varieties, ascending chain condition, descending chain condition. 
@article{SEMR_2019_16_a15,
     author = {S. V. Gusev},
     title = {On the ascending and descending chain conditions in the lattice of monoid varieties},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {983--997},
     publisher = {mathdoc},
     volume = {16},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2019_16_a15/}
}
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S. V. Gusev. On the ascending and descending chain conditions in the lattice of monoid varieties. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 16 (2019), pp. 983-997. http://geodesic.mathdoc.fr/item/SEMR_2019_16_a15/