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...

algebraic number theory. This study reveals hidden structures behind the rational numbers, by using algebraic methods. The notion of algebraic number field relies...

is an algebraic number. Fields of algebraic numbers are also called algebraic number fields, or shortly number fields. Algebraic number theory studies...

algebraic number theory topics. These topics are basic to the field, either as prototypical examples, or as basic objects of study. Algebraic number field...

algebraic number theory, a modulus (plural moduli) (or cycle, or extended ideal) is a formal product of places of a global field (i.e. an algebraic number...

no such polynomial exists then the number is called transcendental. More generally the theory deals with algebraic independence of numbers. A set of numbers...

ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings...

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems...

are much better understood than noncommutative ones. Algebraic geometry and algebraic number theory, which provide many natural examples of commutative...

In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures, which are sets with specific operations...