algebraic extension
61Transcendence degree — In abstract algebra, the transcendence degree of a field extension L / K is a certain rather coarse measure of the size of the extension. Specifically, it is defined as the largest cardinality of an algebraically independent subset of L over K .A …
62Real closed field — In mathematics, a real closed field is a field F in which any of the following equivalent conditions are true:#There is a total order on F making it an ordered field such that, in this ordering, every positive element of F is a square in F and… …
63List of mathematics articles (A) — NOTOC A A Beautiful Mind A Beautiful Mind (book) A Beautiful Mind (film) A Brief History of Time (film) A Course of Pure Mathematics A curious identity involving binomial coefficients A derivation of the discrete Fourier transform A equivalence A …
64p-adic number — In mathematics, and chiefly number theory, the p adic number system for any prime number p extends the ordinary arithmetic of the rational numbers in a way different from the extension of the rational number system to the real and complex number… …
65List 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 …
66P-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 =… …
67Integrality — In commutative algebra, the notions of an element integral over a ring (also called an algebraic integer over the ring), and of an integral extension of rings, are a generalization of the notions in field theory of an element being algebraic over …
68Classical modular curve — In number theory, the classical modular curve is an irreducible plane algebraic curve given by an equation Φn(x, y)=0, where for the j invariant j(τ), x=j(n τ), y=j(τ) is a point on the curve. The curve is sometimes called X0(n), though often… …
69p-adically closed field — In mathematics, a p adically closed field is a field that enjoys a closure property that is a close analogue for p adic fields to what real closure is to the real field. They were introduced by James Ax and Simon B. Kochen in 1965.[1] Contents 1… …
70Field norm — In mathematics, the (field) norm is a mapping defined in field theory, to map elements of a larger field into a smaller one. Contents 1 Formal definitions 2 Example 3 Further properties 4 See also …
