Algebraic number theory information

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...

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

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

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

the complex number 1 + i {\displaystyle 1+i} is algebraic because it is a root of x4 + 4. All integers and rational numbers are algebraic, as are all...

development of the theories of automorphic forms, representation theory of algebraic groups, and more advanced topics in algebraic number theory. The style is...

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

In abstract algebra, an adelic algebraic group is a semitopological group defined by an algebraic group G over a number field K, and the adele ring A...

Zbl 1154.11002. Henri Cohen (1993). A Course In Computational Algebraic Number Theory. Graduate Texts in Mathematics. Vol. 138. Springer-Verlag. doi:10...

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

mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include groups, rings...

numbers are called algebraic number fields and are the main objects of study of algebraic number theory. Another example of a common algebraic extension is...

In abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known...

There are three main branches of algebraic graph theory, involving the use of linear algebra, the use of group theory, and the study of graph invariants...

In algebraic number theory, an algebraic integer is a complex number that is integral over the integers. That is, an algebraic integer is a complex root...

theorem of Galois theory. The use of base fields other than Q is crucial in many areas of mathematics. For example, in algebraic number theory, one often does...

branches like algebraic number theory and algebraic topology. The word algebra itself has several meanings. Algebraic may also refer to: Algebraic data type...

with little algebraic relation simultaneously. From this point of view, operator algebras can be regarded as a generalization of spectral theory of a single...

the scope of algebra broadened beyond a theory of equations to cover diverse types of algebraic operations and algebraic structures. Algebra is relevant...

geometry is roughly the application of techniques from algebraic geometry to problems in number theory. Arithmetic geometry is centered around Diophantine...

In mathematics, class field theory (CFT) is the fundamental branch of algebraic number theory whose goal is to describe all the abelian Galois extensions...

{\displaystyle \mathbb {Q} \left[{\sqrt {-d}}\right]} has class number 1. Equivalently, the ring of algebraic integers of Q [ − d ] {\displaystyle \mathbb {Q} \left[{\sqrt...

an important tool and object of study in commutative algebra, algebraic number theory and algebraic geometry. The prime ideals of the ring of integers are...