Abstract. We examine the problem of determining when a finite Rees quotient of a free monoid has a finite basis for its identities. In [bibjac] and [bibosa] there is shown to be many difficulties associated with this problem but the main examples and theorems there concern the Rees quotients of free monoids on small numbers of generators. Here we extend these results to arbitrary finite generating sets and provide some considerably more general conditions on when a finite Rees quotient of a free monoid is not finitely based. We also introduce the notion of a strongly not finitely based word and construct some examples.

AMS Subject Classification (1991): 20M07, 08B05

Received January 3, 2000. (Registered under 2777/2009.)