On the ascending and descending chain conditions in the lattice of monoid varieties

S. V. Gusev
2019 Sibirskie Elektronnye Matematicheskie Izvestiya  
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. Gusev, S.V., On the ascending and descending chain conditions in the lattice of monoid varieties.
doi:10.33048/semi.2019.16.067 fatcat:mh2lvplfw5gktnidvohltrcs3u