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...

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...

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...

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...

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}...

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...

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...

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...

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

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

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...

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

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...

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...

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...

to a purely formal system as envisaged in Hilbert's program. This dealt a final blow to the heart of Hilbert's program, the hope that consistency could...

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...