论文信息 - A Diophantine Definition of Rational Integers over Some Rings of Algebraic Numbers

A Diophantine Definition of Rational Integers over Some Rings of Algebraic Numbers

The author considers the rings of algebraic numbers integral at all but finitely many primes in the number fields, where it has been previously shown that Hubert's Tenth Problem is undecidable in the rings of algebraic integers, and proves that the problem is still undecidable in the bigger rings by constructing a diophantine definition of rational integers there.

Alexandra Shlapentokh

[1] A diophantine definition of integers in the rings of rational numbers , 1991 .

[2] L. Lipshitz,et al. Diophantine Sets over Some Rings of Algebraic Integers , 1978 .

[3] Hilbert’s tenth problem for quadratic rings , 1975 .

[4] T. Pheidas. Hilbert’s tenth problem for a class of rings of algebraic integers , 1988 .

[5] Martin D. Davis. Hilbert's Tenth Problem is Unsolvable , 1973 .

[6] Alexandra Shlapentokh. Extension of Hilbert's tenth problem to some algebraic number fields , 1989 .

[7] H. N. Shapiro,et al. Diophantine relationships between algebraic number fields , 1989 .

[8] G. Hardy,et al. An Introduction To The Theory Of Numbers Fourth Edition , 1968 .