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We generalize a question of Büchi: Let R be an integral domain, C a subring and k ≥ 2 an integer. Is there an algorithm to decide the solvability in R of any given system of polynomial equations, each of which is linear in the kth powers of the unknowns, with coefficients in C? We state a number-theoretical problem, depending on k, a positive answer to which would imply a negative answer to the question for R = C = ℤ. We reduce a negative answer for k = 2 and for...

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Elimination theory for the ring of algebraic integers.

Erblich euklidische Körper.

Errata to the paper "Remarks of the elementary theories of formal and convergent power series" Fundamenta Mathematicae 105 (1980), pp. 229-239

Existentially closed domains with radical relations.

Extensions of Büchi's problem: Questions of decidability for addition and kth powers

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