splitting extension
1Splitting field — In abstract algebra, a splitting field of a polynomial with coefficients in a field is a smallest field extension of that field over which the polynomial factors (or splits , hence the name) into linear factors. Contents 1 Definition 2 Facts 3 …
2Splitting of prime ideals in Galois extensions — In mathematics, the interplay between the Galois group G of a Galois extension L of a number field K, and the way the prime ideals P of the ring of integers OK factorise as products of prime ideals of OL, provides one of the richest parts of… …
3Extension (mathematics) — In mathematics, the word extension has many uses. See:Analysis* Carathéodory s extension theorem * Continuous linear extension * M. Riesz extension theorem * Krein extension theorem * Hahn Banach theoremAlgebra* Abelian extension * Algebraic… …
4Extension and contraction of ideals — In commutative algebra, the extension and contraction of ideals are operations performed on sets of ideals. Extension of an ideal Let A and B be two commutative rings with unity, and let f : A → B be a (unital) ring homomorphism. If mathfrak{a}… …
5Construction of splitting fields — In mathematics, a splitting field of a polynomial with coefficients in a field is an extension of that field over which the polynomial factors into linear factors. The purpose of this article is to describe an iterative process for constructing… …
6Normal extension — In abstract algebra, an algebraic field extension L/K is said to be normal if L is the splitting field of a family of polynomials in K[X]. Bourbaki calls such an extension a quasi Galois extension. Contents 1 Equivalent properties and examples 2… …
7Field extension — In abstract algebra, field extensions are the main object of study in field theory. The general idea is to start with a base field and construct in some manner a larger field which contains the base field and satisfies additional properties. For… …
8Group extension — In mathematics, a group extension is a general means of describing a group in terms of a particular normal subgroup and quotient group. If Q and N are two groups, then G is an extension of Q by N if there is a short exact sequence:1 ightarrow N… …
9Galois extension — In mathematics, a Galois extension is an algebraic field extension E / F satisfying certain conditions (described below); one also says that the extension is Galois. The significance of being a Galois extension is that the extension has a Galois… …
10New York Tunnel Extension — Pennsylvania Railroad Tunnel under the Hudson River, New York City Overview Type …
