scholarly journals Defining Integers

2011 ◽  
Vol 17 (2) ◽  
pp. 230-251 ◽  
Author(s):  
Alexandra Shlapentokh
Keyword(s):  
North American ◽  
Number Fields ◽  
Rational Numbers ◽  
Plenary Talk ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem ◽  
Rings Of Integers ◽  
Recent Developments ◽  
University Of Notre Dame ◽  
The University

AbstractThis paper surveys the recent developments in the area that grew out of attempts to solve an analog of Hilbert's Tenth Problem for the field of rational numbers and the rings of integers of number fields. It is based on a plenary talk the author gave at the annual North American meeting of ASL at the University of Notre Dame in May of 2009.

Existential definability with bounds on archimedean valuations

2003 ◽  
Vol 68 (3) ◽  
pp. 860-878 ◽  
Author(s):  
Alexandra Shlapentokh
Keyword(s):  
Real Number ◽  
Number Fields ◽  
Algebraic Integers ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem ◽  
Rings Of Algebraic Integers

AbstractWe show that a solution to Hilbert's Tenth Problem in the rings of algebraic integers and bigger subrings of number fields where it is currently not known, is equivalent to a problem of bounding archimedean valuations over non-real number fields.

scholarly journals Hilbert’s Tenth Problem and Mazur’s Conjectures in Complementary Subrings of Number Fields

2011 ◽  
Vol 18 (6) ◽  
pp. 1141-1162 ◽  
Author(s):  
Kirsten Eisenträger ◽  
Graham Everest ◽  
Alexandra Shlapentokh
Keyword(s):  
Number Fields ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem

scholarly journals As easy as $\mathbb {Q}$: Hilbert’s Tenth Problem for subrings of the rationals and number fields

2017 ◽  
Vol 369 (11) ◽  
pp. 8291-8315 ◽  
Author(s):  
Kirsten Eisenträger ◽  
Russell Miller ◽  
Jennifer Park ◽  
Alexandra Shlapentokh
Keyword(s):  
Number Fields ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem

Hilbert's Tenth Problem

2021 ◽  
Vol 52 (2) ◽  
pp. 36-44
Author(s):  
William Gasarch
Keyword(s):  
Short Version ◽  
Hilbert's Tenth Problem ◽  
Hilbert’S Tenth Problem ◽  
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