purely transcendental extension
1Degree of a field extension — In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the size of the extension. The concept plays an important role in many parts of mathematics, including algebra and number theory indeed in any… …
2Field 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… …
3Transcendence 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 …
4Rational 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… …
5Inverse Galois problem — In mathematics, the inverse Galois problem concerns whether or not every finite group appears as the Galois group of some Galois extension of the rational numbers Q. This problem, first posed in the 19th centuryFact|date=February 2007, is… …
6Integral element — In commutative algebra, an element b of a commutative ring B is said to be integral over its subring A if there are such that That is to say, b is a root of a monic polynomial over A.[1] If B consists of elements that are integral over A, then B… …
7Integrality — 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 …
8Emmy Noether — Amalie Emmy Noether Born 23 March 1882(1882 03 23) …
9epistemology — epistemological /i pis teuh meuh loj i keuhl/, adj. epistemologically, adv. epistemologist, n. /i pis teuh mol euh jee/, n. a branch of philosophy that investigates the origin, nature, methods, and limits of human knowledge. [1855 60; < Gk… …
10Henry of Ghent and Duns Scotus — Stephen Dumont LIFE AND WORKS Henry of Ghent Henry of Ghent was arguably the most influential Latin theologian between Thomas Aquinas and Duns Scotus, regent as a leading master of theology at the University of Paris for the better part of the… …
