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...

theory) Hilbert's theorem 90 (number theory) Isomorphism extension theorem (abstract algebra) Joubert's theorem (algebra) Lagrange's theorem (number theory)...

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...

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...

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...

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

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...

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...

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:...

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...

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

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...

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}...

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...

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,...

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...

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...

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

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...

differential equations. Their De Giorgi–Nash theorem on the smoothness of solutions of such equations resolved Hilbert's nineteenth problem on regularity in the...

Philosophical thought experiment Second Borel–Cantelli lemma – Theorem in probability Hilbert's paradox of the Grand Hotel – Thought experiment of infinite...

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...

Noether extended Hilbert's theorem to representations of a finite group over any field; the new case that did not follow from Hilbert's work is when the...

Reeh–Schlieder theorem is a result in relativistic local quantum field theory published by Helmut Reeh and Siegfried Schlieder in 1961. The theorem states that...

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...