One of the classical achievements of the combinatorial group theory is the decidability of the word problem in a finitely generated group with one defining relation. This result was a corollary of a fundamental statement called Freiheitssatz: every equation over a free group is solvable in some extension. This is for solvable and nilpotent groups.
Freiheitssatz has been investigated for other algebraic structures.
Is Freiheitssatz the same concept; namely, the word problem in some literature?