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The word problem is an old and central problem in (computational) grouptheory. It is well-known that the word problem is undecidable in general, butdecidable for specific types of presentations. Consistent polycyclicpresentations are an important class of group presentations with solvable wordproblem. These presentations play a fundamental role in the algorithmic theoryof polycyclic groups. Problems analogous to the word problem arise whencomputing with other algebraic structures. Various aspects of this topic areconsidered in the literature. The aim of this paper is to provide a generalapproach to the topic including polycyclic groups and nilpotent associativealgebras as examples.

The word problem for polycyclic groups and nilpotent associative algebras