Abstract
Let A ∗ be the free monoid of base A and n a fixed positive integer. For any word wϵA ∗ we consider the set [ w] n of all the words which are equivalent to w modulus the congruence θ n generated by the relation x n ∼ x n +1, where x is any word of A ∗. The main result of the paper is that if n>4 then for any word wϵA ∗ the congruence class [ w] n is a regular language. We also prove that the word problem for the quotient monoid M n= A ∗ θ n is recursively solvable.
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