algebraic number field
31Outline of algebraic structures — In universal algebra, a branch of pure mathematics, an algebraic structure is a variety or quasivariety. Abstract algebra is primarily the study of algebraic structures and their properties. Some axiomatic formal systems that are neither… …
32P-adic number — In mathematics, the p adic number systems were first described by Kurt Hensel in 1897 [cite journal | last = Hensel | first = Kurt | title = Über eine neue Begründung der Theorie der algebraischen Zahlen | journal =… …
33Cubic field — In mathematics, specifically the area of algebraic number theory, a cubic field is an algebraic number field of degree three. Contents 1 Definition 2 Examples 3 Galois closure 4 …
34Quadratic field — In algebraic number theory, a quadratic field is an algebraic number field K of degree two over Q. It is easy to show that the map d ↦ Q(√d) is a bijection from the set of all square free integers d ≠ 0, 1 to the set of… …
35Ideal number — In mathematics an ideal number is an algebraic integer which represents an ideal in the ring of integers of a number field; the idea was developed by Ernst Kummer, and led to Richard Dedekind s definition of ideals for rings. An ideal in the ring …
36Monogenic field — In mathematics, a monogenic field is an algebraic number field K for which there exists an element a such that the ring of integers OK is the polynomial ring Z[a]. The powers of such an element a constitute a power integral basis. In a monogenic… …
37Pisot-Vijayaraghavan number — In mathematics, a Pisot Vijayaraghavan number, also called simply a Pisot number or a PV number, is an algebraic integer α which is real and exceeds 1, but such that its conjugate elements are all less than 1 in absolute value. For example, if… …
38Abstract analytic number theory — is a branch of mathematics which takes the ideas and techniques of classical analytic number theory and applies them to a variety of different mathematical fields. The classical prime number theorem serves as a prototypical example, and the… …
39Algebraic topology — is a branch of mathematics which uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism. In many situations this is too much to hope for… …
40Algebraic statistics — is a fairly recent field of statistics which utilizes the tools of algebraic geometry and commutative algebra in order to study problems related to discrete random variables with finite state spaces. Such problems include parameter estimation,… …
