A residually finite associative algebra with an undecidable word problem
Copyright policy )A residually finite associative algebra with an undecidable word problem
For any constructive commutative ring \(k\) with unity, the author constructs a series of examples of a residually finite, finitely generated, recursively defined associative \(k\)-algebra with unity whose word problem is undecidable. This answers a question posed by \textit{L.~A.~Bokut'} [Izv. Vyssh. Uchebn. Zaved., Mat. 1982, No. 11(246), 3-11 (1982; Zbl 0513.17001)].
word problem, residually finite algebras, recursively defined algebras, Decidability of theories and sets of sentences, Applications of logic in associative algebras, associative algebras, Finite rings and finite-dimensional associative algebras, commutative rings, finitely generated algebras, Word problems, etc. in computability and recursion theory, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
word problem, residually finite algebras, recursively defined algebras, Decidability of theories and sets of sentences, Applications of logic in associative algebras, associative algebras, Finite rings and finite-dimensional associative algebras, commutative rings, finitely generated algebras, Word problems, etc. in computability and recursion theory, Finite generation, finite presentability, normal forms (diamond lemma, term-rewriting)
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