In mathematics, the Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states that for any field k...

Mumford conjecture. In this paper Noether also introduced the Noether normalization lemma, showing that a finitely generated domain A over a field k has...

science Normalizing constant, in probability theory a constant to make a non-negative function a probability density function Noether normalization lemma, the...

and at Bryn Mawr College Noether's theorem (or Noether's first theorem) Noether's second theorem Noether normalization lemma Noetherian rings Nöther crater...

finitely generated k-algebra. The result is due to Noether and can be shown using the Noether normalization lemma as follows. It is clear that it is enough to...

{k[x_{0},\ldots ,x_{n}]}{(f_{1}\cdots f_{k},g)}}\right)} Noether normalization lemma Resolution of singularities Eisenbud, D. Commutative Algebra...

also refer to: Noether's second theorem, on infinite-dimensional Lie algebras and differential equations Noether normalization lemma, on finitely generated...

Albert–Brauer–Hasse–Noether theorem Lasker–Noether theorem Noether identities Noether normalization lemma Noether's bound Noether's isomorphism theorems Noether’s problem...

below. The lemma is also a consequence of the Noether normalization lemma. Indeed, by the normalization lemma, K is a finite module over the polynomial ring...

Zassenhaus lemma Gauss's lemma (polynomials) Schwartz–Zippel lemma Artin–Rees lemma Hensel's lemma (commutative rings) Nakayama lemma Noether's normalization lemma...

Sturmian words. Noether normalization lemma The Noether normalization lemma is a result of commutative algebra, introduced by Emmy Noether in 1926. It states...

theorem Primary ideal Primary decomposition and the Lasker–Noether theorem Noether normalization lemma Going up and going down Spectrum of a ring Zariski tangent...

specifically abstract algebra, the isomorphism theorems (also known as Noether's isomorphism theorems) are theorems that describe the relationship among...

extension Q ( B ) / Q ( A ) . {\displaystyle Q(B)/Q(A).} The Noether normalization lemma implies that if R is an integral domain that is a finitely generated...

{\displaystyle k} is of finite type over k {\displaystyle k} . The Noether normalization lemma says, in geometric terms, that every affine scheme X {\displaystyle...

is the projective analog of Noether's normalization lemma. (In fact, it yields a geometric proof of the normalization lemma.) The same procedure can be...

prime ideal of a finitely generated algebra over a field, by the Noether normalization lemma; it also exists when R is complete and contains a field, or when...

two years after the first Negro National League had disbanded Noether normalization lemma — a theorem in commutative algebra No net loss – an environmental...

if R is finitely generated as an algebra (for instance by the Noether normalization lemma). Let R be a Noetherian ring, I an ideal and gr I ⁡ ( R ) = ⨁...

dévissage. Another version of generic freeness can be proved using Noether's normalization lemma. EGA IV2, Théorème 6.9.1 EGA IV2, Corollaire 6.9.3 EGA IV2,...

closed. In Mumford's red book, the theorem is proved by means of Noether's normalization lemma. For an algebraic approach where the generic freeness plays...

\kappa ({\mathfrak {p}})\otimes _{R}{R'}_{{\mathfrak {p}}'}.} By Noether's normalization lemma, the second term on the right side is: dim ⁡ κ ( p ) ⊗ R R ′...

Fitting lemma Schur's lemma Nakayama's lemma Krull–Schmidt theorem Steinitz exchange lemma Jordan–Hölder theorem Artin–Rees lemma Schanuel's lemma Morita...

Sylow theorems Hall subgroup Wreath product Butterfly lemma Center of a group Centralizer and normalizer Characteristic subgroup Commutator Composition series...

containing I has a minimal element, which is a minimal prime over I. Emmy Noether showed that in a Noetherian ring, there are only finitely many minimal...

{\displaystyle u\in T_{n}} such that g = f u {\displaystyle g=fu} . (Noether normalization) If a ⊂ T n {\displaystyle {\mathfrak {a}}\subset T_{n}} is an ideal...

one maximal ideal; this follows from Zorn's lemma. A ring is called Noetherian (in honor of Emmy Noether, who developed this concept) if every ascending...

e^{\frac {i(x-y)^{2}}{2T}},} which, with the same normalization as before (not the sum-squares normalization – this function has a divergent norm), obeys a...

the 20th century David Hilbert, Oskar Bolza, Gilbert Ames Bliss, Emmy Noether, Leonida Tonelli, Henri Lebesgue and Jacques Hadamard among others made...

over itself, in other words every ideal is finitely generated. 3.  Noether normalization represents a finitely generated algebra over a field as a finite...