transcendence degree
21Algebraic 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… …
22Rational variety — In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to projective space of some dimension over K. This is a question on its function field: is it up to isomorphism the field of all… …
23Dimension 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… …
24Global field — In mathematics, the term global field refers to either of the following:*a number field, i.e., a finite extension of Q or *the function field of an algebraic curve over a finite field, i.e., a finitely generated field of characteristic p >0 of… …
25List of abstract algebra topics — Abstract algebra is the subject area of mathematics that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras. The phrase abstract algebra was coined at the turn of the 20th century to distinguish this …
26Closure operator — In mathematics, a closure operator on a set S is a function cl: P(S) → P(S) from the power set of S to itself which satisfies the following conditions for all sets X,Y ⊆ S. X ⊆ cl(X) (cl is extensive) X ⊆ Y implies cl(X) ⊆ cl(Y)   (cl… …
27Algebraic geometry and analytic geometry — In mathematics, algebraic geometry and analytic geometry are two closely related subjects. While algebraic geometry studies algebraic varieties, analytic geometry deals with complex manifolds and the more general analytic spaces defined locally… …
28Morley's categoricity theorem — Vaught s test redirects here. Not to be confused with the Tarski–Vaught test. Categorical theory redirects here. Not to be confused with Category Theory. In model theory, a branch of mathematical logic, a theory is κ categorical (or categorical… …
29Geometric invariant theory — In mathematics Geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces. It was developed by David Mumford in 1965, using ideas from the paper… …
30Compact Riemann surface — In mathematics, a compact Riemann surface is a complex manifold of dimension one that is a compact space. Riemann surfaces are generally classified first into the compact (those that are closed manifolds) and the open (the rest, which from the… …
