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Diophantine sets of polynomials over number fields

Jeroen Demeyer UGent (2010) PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 138(8). p.2715-2728
abstract
Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T]. We show that the set of polynomials with integer coefficients is diophantine over R[7]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T](k) is diophantine over R[T].
Please use this url to cite or link to this publication:
author
organization
year
type
journalArticle (original)
publication status
published
subject
keyword
Hilbert's Tenth Problem, RECURSIVELY-ENUMERABLE SETS, Recursively enumerable set, Diophantine set, HILBERTS 10TH PROBLEM, P-ADIC FIELDS, FINITE-FIELD, RINGS
journal title
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Proc. Amer. Math. Soc.
volume
138
issue
8
pages
2715 - 2728
Web of Science type
Article
Web of Science id
000280305000008
JCR category
MATHEMATICS
JCR impact factor
0.601 (2010)
JCR rank
132/276 (2010)
JCR quartile
2 (2010)
ISSN
0002-9939
DOI
10.1090/S0002-9939-10-10329-3
language
English
UGent publication?
yes
classification
A1
copyright statement
I have transferred the copyright for this publication to the publisher
id
1073291
handle
http://hdl.handle.net/1854/LU-1073291
date created
2010-11-12 11:56:39
date last changed
2016-12-19 15:44:28
@article{1073291,
  abstract     = {Let R be a number field or a recursive subring of a number field and consider the polynomial ring R[T]. We show that the set of polynomials with integer coefficients is diophantine over R[7]. Applying a result by Denef, this implies that every recursively enumerable subset of R[T](k) is diophantine over R[T].},
  author       = {Demeyer, Jeroen},
  issn         = {0002-9939},
  journal      = {PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY},
  keyword      = {Hilbert's Tenth Problem,RECURSIVELY-ENUMERABLE SETS,Recursively enumerable set,Diophantine set,HILBERTS 10TH PROBLEM,P-ADIC FIELDS,FINITE-FIELD,RINGS},
  language     = {eng},
  number       = {8},
  pages        = {2715--2728},
  title        = {Diophantine sets of polynomials over number fields},
  url          = {http://dx.doi.org/10.1090/S0002-9939-10-10329-3},
  volume       = {138},
  year         = {2010},
}

Chicago
Demeyer, Jeroen. 2010. “Diophantine Sets of Polynomials over Number Fields.” Proceedings of the American Mathematical Society 138 (8): 2715–2728.
APA
Demeyer, Jeroen. (2010). Diophantine sets of polynomials over number fields. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 138(8), 2715–2728.
Vancouver
1.
Demeyer J. Diophantine sets of polynomials over number fields. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY. 2010;138(8):2715–28.
MLA
Demeyer, Jeroen. “Diophantine Sets of Polynomials over Number Fields.” PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 138.8 (2010): 2715–2728. Print.