This article is cited in 7 papers

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

Abstract: 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.

UDC: 512.532.2

MSC: 20M07, 08B15

Received February 13, 2019, published August 5, 2019

Language: English

DOI: 10.33048/semi.2019.16.067

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