In abstract algebra, Hilbert's Theorem 90 (or Satz 90) is an important result on cyclic extensions of fields (or to one of its generalizations) that leads...

\mathbb {R} ^{3}} Hilbert's Theorem 90, an important result on cyclic extensions of fields that leads to Kummer theory Hilbert's basis theorem, in commutative...

theorem Hilbert's Nullstellensatz Hilbert's theorem (differential geometry) Hilbert's Theorem 90 Hilbert's syzygy theorem Hilbert–Speiser theorem Brouwer–Hilbert...

role in many aspects of Hilbert space theory. Exact analogs of the Pythagorean theorem and parallelogram law hold in a Hilbert space. At a deeper level...

theorem Hilbert–Smith conjecture Hilbert–Speiser theorem Hilbert–Waring theorem Hilbert's arithmetic of ends Hilbert's axioms Hilbert's basis theorem...

additive counterparts of the methods involved in Kummer theory, such as Hilbert's theorem 90 and additive Galois cohomology. These extensions are called Artin–Schreier...

second cohomology group is isomorphic to the Brauer group of K (by Hilbert's theorem 90, its first cohomology group is zero). If X is a smooth proper scheme...

The corresponding result for the multiplicative group is known as Hilbert's Theorem 90, and was known before 1900. Kummer theory was another such early...

which has come to be known as the Riemann–Hilbert problem. Hilbert's work was mainly concerned with the Hilbert transform for functions defined on the circle...

acting on a field L and A=L×, then this is a field formation by Hilbert's theorem 90. The most important examples of class formations (arranged roughly...

exact sequence in cohomology for a field F {\displaystyle F} . Since Hilbert's Theorem 90 implies H 1 ( F , G m ) = 0 {\displaystyle H^{1}(F,\mathbb {G} _{m})=0}...

irreducibility theorem (number theory) Hilbert's syzygy theorem (commutative algebra) Hilbert's theorem (differential geometry) Hilbert's theorem 90 (number...

classes. Part 2 covers Galois number fields, including in particular Hilbert's theorem 90. Part 3 covers quadratic number fields, including the theory of genera...

Diophantus II.VIII Eisenstein triple Euler brick Heronian triangle Hilbert's theorem 90 Integer triangle Modular arithmetic Nonhypotenuse number Plimpton...

while the kernel is trivial because H1(GLn) = {1} by an extension of Hilbert's Theorem 90. Therefore, Severi–Brauer varieties can be faithfully represented...

when n is 0 is trivial, and the case when n = 1 follows easily from Hilbert's Theorem 90. The case n = 2 and ℓ = 2 was proved by (Merkurjev 1981) harv error:...

Bell's theorem is a term encompassing a number of closely related results in physics, all of which determine that quantum mechanics is incompatible with...

In mathematics, the Pythagorean theorem or Pythagoras' theorem is a fundamental relation in Euclidean geometry between the three sides of a right triangle...

H^{1}\left(L,{\overline {K}}^{\times }\right)[m]\xrightarrow {} 0} By Hilbert's Theorem 90 H 1 ( L , K ¯ × ) = 0 {\displaystyle H^{1}\left(L,{\overline {K}}^{\times...

system that generates theorems from axioms and inference rules, especially if the only inference rule is modus ponens. Every Hilbert system is an axiomatic...

result on Hilbert's plan to prove the consistency of mathematics. It is likely that all mathematicians ultimately would have accepted Hilbert's approach...

isomorphic to the Galois cohomology group H 1(K, K*) which vanishes by Hilbert's theorem 90. Therefore, the long exact sequence of étale cohomology groups gives...

Brouwer's fixed-point theorem is a fixed-point theorem in topology, named after L. E. J. (Bertus) Brouwer. It states that for any continuous function f...

using a more explicit assumption. In Hilbert's axiomatization of geometry this statement is given as a theorem, but only after much groundwork. One may...

Hess Hilbert's basis theorem Hilbert's axioms Hilbert function Hilbert's irreducibility theorem Hilbert's syzygy theorem Hilbert's Theorem 90 Hilbert's theorem...

differential equations in the complex plane. Several existence theorems for Riemann–Hilbert problems have been produced by Mark Krein, Israel Gohberg and...

cohomology was formulated in 1943–45. The first theorem of the subject can be identified as Hilbert's Theorem 90 in 1897; this was recast into Emmy Noether's...

In mathematics, Hilbert's fourth problem in the 1900 list of Hilbert's problems is a foundational question in geometry. In one statement derived from the...

Halmos's A Hilbert Space Problem Book (see the references).[citation needed] Parseval's identity leads immediately to the following theorem: Theorem. Let V...

Hilbert space, is the space of all unit vectors in Hilbert space up to the equivalence relation of differing by a phase factor. By Wigner's theorem,...