The number of solutions of a Diophantine equation over a recursive ring (Q2855895)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: The number of solutions of a Diophantine equation over a recursive ring |
scientific article; zbMATH DE number 6218146
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The number of solutions of a Diophantine equation over a recursive ring |
scientific article; zbMATH DE number 6218146 |
Statements
23 October 2013
0 references
Hilbert's tenth problem
0 references
recursive ring
0 references
The number of solutions of a Diophantine equation over a recursive ring (English)
0 references
The paper under review proves the following result. If \(R\) is a recursive ring (i.e. a ring decidable as a set and with recursive graphs of addition and multiplication) whose fraction field is not algebraically closed and such that Hilbert's Tenth Problem is not decidable over \(R\), then there is no algorithm to determine the number of \(R\)-solutions of an arbitrary polynomial equation with coefficients in \(R\). Here the we allow the number of solutions to be equal to \(\infty\) also. Such a result was previously obtained by Martin Davis for \(R= \mathbb Z\).
0 references
