LEE MONOIDS ARE NONFINITELY BASED WHILE THE SETS OF THEIR ISOTERMS ARE FINITELY BASED

摘要

We establish a new sufficient condition under which a monoid is nonfinitely based and apply this condition to Lee monoids L-l(1), obtained by adjoining an identity element to the semigroup generated by two idempotents a and b with the relation 0 = abab ... (length l). We show that every monoid M which generates a variety containing L-5(1) and is contained in the variety generated by L-l(1) for some l = 5 is nonfinitely based. We establish this result by analysing tau-terms for M, where tau is a certain nontrivial congruence on the free semigroup. We also show that if tau is the trivial congruence on the free semigroup and l = 5, then the tau-terms (isoterms) for L-l(1) carry no information about the nonfinite basis property of L-l(1).