Diophantine undecidability for addition and divisibility in
polynomial rings

Thanases Pheidas

doi:10.4064/fm182-3-2

Instytut Matematyczny Polskiej Akademii Nauk / Institute of Mathematics / Publishing house / Journals and Serials / Fundamenta Mathematicae / All issues

Diophantine undecidability for addition and divisibility in polynomial rings

Volume 182 / 2004

Thanases Pheidas Fundamenta Mathematicae 182 (2004), 205-220 MSC: Primary 03B25, 12L05; Secondary 11U05. DOI: 10.4064/fm182-3-2

Abstract

We prove that the positive-existential theory of addition and divisibility in a ring of polynomials in two variables $A[t_1,t_2 ]$ over an integral domain $A$ is undecidable and that the universal-existential theory of $A[t_1]$ is undecidable.

Authors

Thanases PheidasDepartment of Mathematics
University of Crete
71409 Heraklion, Greece
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