THE WORD PROBLEM FOR NILPOTENT INVERSE MONOIDS

The concept of Ic-nilpotency is adapted for inverse semigroups and N-k(X) is defined as the largest k-nilpotent Rees quotient of the free inverse monoid on X. The membership problem is solved for a certain class of ideals of quasifree inverse monoids. As a consequence, the word problem is shown to be decidable for every finite relation on N-k(X), producing an unusual example of total decidability.