algebraic number theory
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English[edit]
Etymology[edit]
Blend of algebraic number + number theory. Possibly (alternatively or also) a calque of German algebraische Zahlentheorie.
Noun[edit]
algebraic number theory (uncountable)
 (mathematics, number theory) The branch of number theory in which numbertheoretic questions are expressed in terms of properties of algebraic number fields or related objects, and studied using techniques from algebra.
 1998, Norbert Klingen, Arithmetical Similarities: Prime Decomposition and Finite Group Theory, Oxford University Press (Clarendon Press), page 241,
 As is wellknown in algebraic number theory, there is a farreaching analogy between number fields and algebraic function fields in one variable with finite constant field.
 2008, Steven H. Weintraub, Factorization: Unique and Otherwise, CRC Press, page 143,
 The field of mathematics that these generalize to is known as algebraic number theory. As a matter of historical fact, our development here parallels the development of algebraic number theory.
 2013, Mak Trifković, Algebraic Theory of Quadratic Numbers, Springer, page v,
 Elementary arithmetic studies divisibility and factorization of ordinary integers, Algebraic number theory considers the same questions for algebraic numbers, solutions to polynomial equations with integer coefficients. In this setting, (un)fortunately, the uniqueness of prime factorization no longer holds. Remedying and measuring its failure is the starting point of algebraic number theory.
 1998, Norbert Klingen, Arithmetical Similarities: Prime Decomposition and Finite Group Theory, Oxford University Press (Clarendon Press), page 241,
Translations[edit]
branch of number theory concerning algebraic number fields


See also[edit]
Further reading[edit]
 Algebraic number field on Wikipedia.Wikipedia
 Number theory#Algebraic number theory on Wikipedia.Wikipedia
 Ring of integers on Wikipedia.Wikipedia
 Algebraic number theory on Encyclopedia of Mathematics
 Algebraic Number Theory on Wolfram MathWorld