The Variety Generated by All Monoids of Order Four Is Finitely Based
Monoid, Semigroup, Variety, Finitely based
It is known that the variety Mn generated by all monoids of order n is finitely based if n ≤ 3 and non-finitely based if n ≥ 6. The present article establishes the finite basis property of the variety M4. This leaves M5 as the last open case in the finite basis problem for the varieties Mn.
Lee, Edmond W. H. and Li, Jian Rong, "The Variety Generated by All Monoids of Order Four Is Finitely Based" (2015). Mathematics Faculty Articles. 17.