Lee monoids are nonfinitely based while the sets of their isoterms are finitely based

We establish a new sufficient condition under which a monoid is nonfinitely based and apply this condition to Lee monoids , obtained by adjoining an identity element to the semigroup generated by two idempotents and with the relation (length ). We show that every monoid which generates a variety containing and is contained in the variety generated by for some is nonfinitely based. We establish this result by analysing -terms for , where is a certain nontrivial congruence on the free semigroup. We also show that if is the trivial congruence on the free semigroup and , then the -terms (isoterms) for carry no information about the nonfinite basis property of .