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A diophantine definition of integers in the rings of rational numbers
Author(s) -
Shlapentokh Alexandra
Publication year - 1991
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.3160440706
Subject(s) - diophantine equation , mathematics , diophantine set , ring (chemistry) , diophantine geometry , discrete mathematics , recursively enumerable language , set (abstract data type) , maximal set , rational number , pure mathematics , computer science , chemistry , organic chemistry , programming language
The author considers rings of rational numbers which are integral at all the primes except, possibly, primes contained in a finite set. In such rings a Diophantine definition of ℤ is constructed to show that all the recursively enumerable subsets of the ring are Diophantine.