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algebraic number theory
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Within Vinony's link graph, algebraic number theory is referenced by 454 other articles, and connects out to Springer Science+Business Media, integer and rational number.
It sits within the topics Algebraic number theory and Number theory.
Its subject is documented across 38 Wikipedia language editions.
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Encyclopedic overview
Title page of the first edition of Disquisitiones Arithmeticae, one of the founding works of modern algebraic number theory
Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations. Number-theoretic questions are expressed in terms of properties of algebraic objects such as algebraic number fields and their rings of integers, finite fields, and function fields. These properties, such as whether a ring admits unique factorization, the behavior of ideals, and the Galois groups of fields, can resolve questions of primary importance in number theory, like the existence of solutions to Diophantine equations.
Excerpted from Wikipedia’s “algebraic number theory” article, available under the CC BY-SA 4.0 licence.