Ernst Kummer (2181 bytes)
1: ...ian]]. Highly skilled in [[applied mathematics]], Kummer trained German army officers in [[ballistics]]; a...
5: ...rgeometric series]] (contiguity relations). The [[Kummer surface]] results from taking the quotient of a t...
7: ==Kummer and Fermat's Last Theorem==
9: ...' arose here. He studied what were later called [[Kummer extension]]s of [[field (mathematics)|fields]]: t...
15: .../Mathematicians/Kummer.html Source for more Ernst Kummer information]

Kummer theory (3094 bytes)
2: In [[mathematics]], a '''Kummer extension''' of [[field (mathematics)|fields]] is...
11: ... true if ''K'' has [[characteristic]] ≠ 2. The Kummer extensions in this case are all '''quadratic exte...
15: ...hen ''K'' has characteristic 2, there are no such Kummer extensions.
17: Taking ''n'' = 3, there are no degree three Kummer extensions of the [[rational number]] field ''Q''...
21: ... is a [[separable polynomial]]. Then ''L/K'' is a Kummer extension.

Regular prime (1970 bytes)
1: ...}. Regular primes were first described by [[Ernst Kummer]].
13: Historically, regular primes were considered by Kummer since he was able to prove that [[Fermat's last t...

Abelian extension (1607 bytes)
5: ...belian Galois group as semi-direct product. The [[Kummer theory]] gives a complete description of the abel...

K3 surface (2165 bytes)
1: ... — it is after three algebraic geometers, [[Kummer]], [[Kähler]] and [[Kunihiko Kodaira|Kodaira]], a...
5: A '''Kummer surface''' is the quotient of a two-dimensional [...

Law of small numbers (544 bytes)
7: ...ter (one example in [[number theory]] being the [[Kummer conjecture on cubic Gauss sums]]);

Carl Wilhelm Borchardt (598 bytes)
5: ... by Gauss and Lagrange. He generalised results of Kummer on equations determining the secular disturbances...

Arthur Moritz Schönflies (1003 bytes)
1: ... and for work in [[topology]]. He studied under [[Kummer]] and [[Weierstrass]], and was influenced by [[Fe...

Iwasawa theory (3139 bytes)
10: ...class group of K had already been identified by [[Kummer]], as the main obstruction to the direct proof of...
14: ...theory had prospects of moving ahead finally from Kummer's century-old results on [[regular prime]]s.

The Early November (741 bytes)
9: *Jeff Kummer - Drums

Algebraic number field (899 bytes)
17: *[[Kummer extension]]

Class field theory (3281 bytes)
11: ...d completions, the theory of [[cyclotomic]] and [[Kummer extension]]s, conjectures of [[Hilbert]] and proo...

Ideal class group (8525 bytes)
9: ...s as part of the '''ideal class group''': in fact Kummer had isolated the ''p''-[[torsion subgroup|torsion...
11: ...] formulated the concept of [[ring ideal|ideal]], Kummer having worked in a different way. At this point t...

Barry Mazur (1323 bytes)
5: ...l, a paper which acted as an abstraction of Ernst Kummer's theory of ideals. This paper was critical in in...

Riesz function (5714 bytes)
37: Using Kummer's method for accelerating convergence gives
46: ...stified by absolute convergence. We may now apply Kummer's method again, and write

Adam's Mark (1319 bytes)
1: ...hain was founded in the early [[1970s]] by [[Fred Kummer]] and the chain is currently owned by HBE, Inc., ...

Weil pairing (2229 bytes)
7: ... and ''Q'' of order ''n'' on ''E'', by means of [[Kummer theory]].

Glossary of field theory (6514 bytes)
83: ; '''[[Kummer theory]]''' : The Galois theory of taking ''n''-t...
85: ...heier theory]]''' : Covers an exceptional case of Kummer theory, in characteristic ''p''.

Ideal number (2469 bytes)
1: ...f a [[number field]]; the idea was developed by [[Kummer]] while trying to solve [[Fermat's last theorem]]...

Bernoulli number (7642 bytes)
63: ...p arithmetical properties, a fact discovered by [[Kummer]] in his work on [[Fermat's last theorem]].
65: ...p]]s of [[cyclotomic field]]s by the a theorem of Kummer and its strengthening in the [[Herbrand-Ribet the...

<< Prev 20 Result Pages:   1  2  3  4  5  6  7  8  9  10  Next 20 >>