algebraic number theory

Hello, you have come here looking for the meaning of the word algebraic number theory. In DICTIOUS you will not only get to know all the dictionary meanings for the word algebraic number theory, but we will also tell you about its etymology, its characteristics and you will know how to say algebraic number theory in singular and plural. Everything you need to know about the word algebraic number theory you have here. The definition of the word algebraic number theory will help you to be more precise and correct when speaking or writing your texts. Knowing the definition ofalgebraic number theory, as well as those of other words, enriches your vocabulary and provides you with more and better linguistic resources.

English

English Wikipedia has an article on:
Wikipedia

Etymology

Blend of algebraic number +‎ number theory. Possibly (alternatively or also) a calque of German algebraische Zahlentheorie.

Noun

algebraic number theory (uncountable)

  1. (mathematics, number theory) The branch of number theory in which number-theoretic 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 well-known in algebraic number theory, there is a far-reaching 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.

Translations

See also

Further reading

Wikious
Boobota
Sagapedia