irreducible variety
1Irreducible component — In mathematics, the concept of irreducible component is used to make formal the idea that a set such as defined by the equation: XY = 0is the union of the two lines: X = 0and : Y = 0.The notion of irreducibility is stronger than connectedness.… …
2Irreducible (mathematics) — In mathematics, the term irreducible is used in several ways. * In abstract algebra, irreducible can be an abbreviation for irreducible element; for example an irreducible polynomial. * In representation theory, an irreducible representation is a …
3Subdirect irreducible — In algebra, a subdirect irreducible is an algebra that cannot be factored as a subdirect product of simpler algebras. Subdirect irreducibles play a somewhat analogous role in algebra to primes in number theory. TOC =Definition=In algebra, a… …
4Algebraic variety — This article is about algebraic varieties. For the term a variety of algebras , and an explanation of the difference between a variety of algebras and an algebraic variety, see variety (universal algebra). The twisted cubic is a projective… …
5Absolutely irreducible — In mathematics, absolutely irreducible is a term applied to linear representations or algebraic varieties over a field. It means that the object in question remains irreducible, even after any finite extension of the field of coefficients. In… …
6Dimension of an algebraic variety — In mathematics, the dimension of an algebraic variety V in algebraic geometry is defined, informally speaking, as the number of independent rational functions that exist on V. For example, an algebraic curve has by definition dimension 1. That… …
7Norm variety — In mathematics, a norm variety is a particular type of algebraic variety V over a field F, introduced for the purposes of algebraic K theory by Voevodsky. The idea is to relate Milnor K theory of F to geometric objects V, having function fields… …
8Regular chain — In computer algebra, a regular chain is a particular kind of triangular set in a multivariate polynomial ring over a field. It enhances the notion of characteristic set. Introduction Given a linear system, one can convert it to a triangular… …
9Étale cohomology — In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil… …
10Pseudo algebraically closed field — In mathematics, a field K is pseudo algebraically closed (usually abbreviated by PAC) if one of the following equivalent conditions holds:*Each absolutely irreducible variety V defined over K has a K rational point. *Each absolutely irreducible… …
