Undecidability of existential theories of rings and fields: A survey (Q2715529)
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scientific article; zbMATH DE number 1607960
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Undecidability of existential theories of rings and fields: A survey |
scientific article; zbMATH DE number 1607960 |
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21 March 2002
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fields of algebraic functions
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rings of analytic functions
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fields of meromorphic functions
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existential theories
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undecidability
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Hilbert's tenth problem
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diophantine polynomial
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decidability
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diophantine theories
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Undecidability of existential theories of rings and fields: A survey (English)
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The aim of the reviewed paper is to give an overview of results and problems connected with Hilbert's tenth problem for various rings and fields.NEWLINENEWLINENEWLINELet \(R\) be a ring, \(L\) be a first-order language of ring theory which includes symbols for some elements of \(R\). A diophantine polynomial in \(L\) over \(R\) is a polynomial whose coefficients are in the subring of \(R\) which is generated by such elements. If \(P\) is a diophantine polynomial in \(L\), \(P=0\) is a diophantine equation in \(L\).NEWLINENEWLINENEWLINEThe emphasis is on the decidability problem for existential and diophantine theories of rings and fields of algebraic and meromorphic functions.NEWLINENEWLINEFor the entire collection see [Zbl 0955.00034].
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