In mathematics, a transcendental extension L / K {\displaystyle L/K} is a field extension such that there exists an element in the field L {\displaystyle...

purely transcendental—a class of such extensions take the form L/K where both L and K are algebraically closed. If L/K is purely transcendental and S is...

a transcendental extension, it is natural to use the fact that every field extension is an algebraic extension of a purely transcendental extension. This...

coefficients in K. A field extension that is not algebraic, is said to be transcendental, and must contain transcendental elements, that is, elements...

transcendental numbers are π and e. The quality of a number being transcendental is called transcendence. Though only a few classes of transcendental...

The Transcendental Meditation (TM) technique is that associated with Transcendental Meditation, developed by the Indian spiritual figure Maharishi Mahesh...

In mathematics, a transcendental function is an analytic function that does not satisfy a polynomial equation whose coefficients are functions of the independent...

isomorphism that fixes F. Transcendental Those elements of an extension field of F that are not algebraic over F are transcendental over F. Algebraically...

field extension C(T)/C, where C(T) is the field of rational functions over C, has infinite degree (indeed it is a purely transcendental extension). This...

or general system of ends. The speculative extension of reason is severely limited in the transcendental dialectics of the Critique of Pure Reason, which...

extensions are also described as purely transcendental. More precisely, the rationality question for the field extension K ⊂ L {\displaystyle K\subset L} is...

transcendental element, an element of a field extension that is not the root of any polynomial with coefficients from the base field Transcendental function...

{\displaystyle G} is called a logarithmic extension of F {\displaystyle F} if G {\displaystyle G} is a simple transcendental extension of F {\displaystyle F} (that...

Transcendental number theory is a branch of number theory that investigates transcendental numbers (numbers that are not solutions of any polynomial equation...

are called transcendental over K. These notions generalize the algebraic numbers and the transcendental numbers (where the field extension is C/Q, with...

In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendence of numbers. It states...

K[y1,..., ym]. Thus the extension K ⊂ A can be written as a composite K ⊂ B ⊂ A where K ⊂ B is a purely transcendental extension and B ⊂ A is finite. In...

The Transcendental Meditation movement (TM) are programs and organizations that promote the Transcendental Meditation technique founded by Maharishi Mahesh...

indeterminates over k {\displaystyle k} , or in other words a pure transcendental extension of k {\displaystyle k} , with transcendence degree n {\displaystyle...

is transcendental over K, K ( X ) ( X p ) ⊃ K ( X ) {\displaystyle K(X)({\sqrt[{p}]{X}})\supset K(X)} is a non-separable algebraic field extension. In...

solutions used in extensions of the algebra. By starting with the field of rational functions, two special types of transcendental extensions (the logarithm...

(purely transcendental extensions) and algebraic extensions. A field is algebraically closed if it does not have any strictly bigger algebraic extensions or...

closed field is regular. An extension is regular if and only if it is separable and primary. A purely transcendental extension of a field is regular. There...

permutation group Sn acting on the field k(x1, ..., xn) always is a pure transcendental extension of the field k. (She first mentioned this problem in a 1913 paper...

{\displaystyle K} are by necessity transcendental over K {\displaystyle K} , and over all of the field extensions over K {\displaystyle K} generated by...

complex numbers that are not algebraic, such as π and e, are called transcendental numbers. The set of algebraic (complex) numbers is countably infinite...

his retirement in 1987. Deleuze's outlook on life was sympathetic to transcendental ideas, "nature as god" ethics, and the monist experience. Some of the...

FMA4 Advanced Vector Extensions (AVX, also known as Gesher New Instructions and then Sandy Bridge New Instructions) are SIMD extensions to the x86 instruction...

In mathematics, specifically transcendental number theory, Schanuel's conjecture is a conjecture made by Stephen Schanuel in the 1960s concerning the transcendence...

in a purely transcendental extension to the multivariate case over the ground field (see below). From coefficients in an algebraic extension to coefficients...