A residually finite associative algebra with an undecidable word problem

For any constructive commutative ring k with unity, we furnish an example of a residually finite, finitely generated, recursively defined associative k-algebra with unity whose word problem is undecidable. This answers a question of Bokut’ in 3]. Translated fromAlgebra i Logika, Vol. 39, No. 4, pp. 441–451, July–August, 2000.