The Smallest Monoid that Generates a Non-Cross Variety
Journal of Xiamen University (Natural Science)
Monoid, Variety, Cross Variety
A monoid variety is a class of monoids that is closed under the formation of homomorphic images, submonoids, and arbitrary direct products. A finitely generated, finitely based variety of monoids that contains only finitely many subvarieties is a Cross monoid variety. The 5-element monoid M5 is first shown to generate a non-Cross monoid variety. Then it is shown that, up to isomorphism and anti-isomorphism, any monoid of order five or less different from M5 generates a Cross monoid variety. Therefore up to isomorphism and anti-isomorphism, M5 is the only smallest monoid that generates a non-Cross monoid variety.
Lee, Edmond W. H. and Zhang, Wen Ting, "The Smallest Monoid that Generates a Non-Cross Variety" (2014). Mathematics Faculty Articles. 148.