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The Number Theory of Algebraic Curves

2008
This chapter investigates algebraic curves from the point of view of their function fields, using methods analogous to those used in studying algebraic number fields.
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Applications to Algebraic Number Theory

1990
Let Z denote the ring of integers. An algebraic number field is an extension of Z of finite degree. Since Z is a natural ring, divisor theory applies to algebraic number fields.
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Number Theory and Algebra

2003
Jeffrey Shallit, Jean-Paul Allouche
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The origins of algebraic number theory

1991
In his effort to construct a theory of biquadratic residues analogous to the theory of quadratic residues (Chapter 1), Gauss realised that it would be necessary to pass from the domain ℤ of integers to the domain $$z\left[ {\sqrt { - 1} } \right]$$ of numbers of the form \(x + y\sqrt {{ - 1}}\) with x,y ∈ℤ.
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Algebraic number theory.

Abstracts from the workshop held June 19--25, 2011; Vol. 8, no. 2, 1709-1768, 2011
B. Howard   +3 more
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ALGEBRAIC NUMBER THEORY

Journal of the London Mathematical Society, 1969
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