Diophantine properties of finite commutative rings

Archive for Mathematical Logic 42 (3):293-302 (2003)
  Copy   BIBTEX

Abstract

Simple observations on diophantine definability over finite commutative rings lead to a characterization of those rings in terms of their diophantine behavior

Categories

Keywords

Reprint years

DOI

10.1007/s001530100130

Links

PhilArchive



    Upload a copy of this work     Papers currently archived: 91,164

External links

Setup an account with your affiliations in order to access resources via your University's proxy server

Through your library

My notes

Similar books and articles

Diophantine equivalence and countable rings.Alexandra Shlapentokh - 1994 - Journal of Symbolic Logic 59 (3):1068-1095.
Diophantine relations between rings of s-integers of fields of algebraic functions in one variable over constant fields of positive characteristic.Alexandra Shlapentokh - 1993 - Journal of Symbolic Logic 58 (1):158-192.
Commutative rings whose ideals form an MV‐algebra.Lawrence P. Belluce & Antonio Di Nola - 2009 - Mathematical Logic Quarterly 55 (5):468-486.
Rings of algebraic numbers in infinite extensions of $${\mathbb {Q}}$$ and elliptic curves retaining their rank.Alexandra Shlapentokh - 2009 - Archive for Mathematical Logic 48 (1):77-114.
On Boolean algebras and integrally closed commutative regular rings.Misao Nagayama - 1992 - Journal of Symbolic Logic 57 (4):1305-1318.
A hierarchy of tree-automatic structures.Olivier Finkel & Stevo Todorčević - 2012 - Journal of Symbolic Logic 77 (1):350-368.
Rings which admit elimination of quantifiers.Bruce I. Rose - 1978 - Journal of Symbolic Logic 43 (1):92-112.
Towards the decidability of the theory of modules over finite commutative rings.Gena Puninski & Carlo Toffalori - 2009 - Annals of Pure and Applied Logic 159 (1-2):49-70.
On Finite Approximations of Topological Algebraic Systems.L. Yu Glebsky, E. I. Gordon & C. Ward Hensen - 2007 - Journal of Symbolic Logic 72 (1):1 - 25.
Review: Martin Davis, Hilary Putnam, Diophantine Sets Over Polynomial Rings. [REVIEW]H. B. Enderton - 1972 - Journal of Symbolic Logic 37 (3):602-603.
A Diophantine definition of rational integers over some rings of algebraic numbers.Alexandra Shlapentokh - 1992 - Notre Dame Journal of Formal Logic 33 (3):299-321.
Diophantine undecidability in some rings of algebraic numbers of totally real infinite extensions of Q.Alexandra Shlapentokh - 1994 - Annals of Pure and Applied Logic 68 (3):299-325.
An Undecidable Property of Recurrent Double Sequences.Mihai Prunescu - 2008 - Notre Dame Journal of Formal Logic 49 (2):143-151.
Hilbert's Tenth Problem for Rings of Rational Functions.Karim Zahidi - 2002 - Notre Dame Journal of Formal Logic 43 (3):181-192.

Analytics

Added to PP
2013-11-23

Downloads
92 (#179,628)

6 months
5 (#526,961)

Historical graph of downloads
How can I increase my downloads?

Citations of this work

No citations found.

Add more citations

References found in this work

No references found.

Add more references