Abstract
The concept ofk-nilpotency is adapted for inverse semigroups andNk(X) is defined as the largestk-nilpotent Rees quotient of the free inverse monoid onX. 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 onNk(X), producing an unusual example of total decidability.
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