About 10,300 results
|This is known as Kummer's lemma. The proof is a brief addition to the argument |
of the preceding section. In the preceding section it was shown that if e(a) is a
unit of the form ± a (1 — aa)x'(\ - a2a)"2 • • • (1 - o^a)**, and if e(a) = c mod X
where c ...
|The reader is encouraged to solve Exercise 5.39 on page 243, which is related to |
the following lemma. Recall, as cited on page 151, that p is regular if p hOF
where F = Q(ζp). Lemma 5.11 — Kummer's Lemma Let p be a regular prime, and
|(9.22) Kummer's lemma. Let e = e2n'lp where p is an odd prime. Then every unit |
in the ring Z[e] can be written as a product of a real unit and a power of e.
ASSUMING this lemma for the time being we can now prove Kummer's
|Kummer's proof follows the outline of the proof of Theorem 3-2.6; the first case is |
handled with the aid of congruences modulo λp and the second case with the aid
of a descent where Kummer's lemma on the units of a cyclotomic field plays a ...
|As for the actual computation of the class number, Kummer ment ioned an |
impending publication by Ci richlet, which would treat this question. ... [This
would be proved later by Kummer himself and it is now known as Kummer's
lemma on units.
|A sequence of polynomials is defined and using it, a theorem equivalent to |
Kummer's lemma is proved. Based on this, a criterion is formed which is an
improvement of Krasner's result for the first case of Fermat's Last Theorem. This
|... 281 Krull topology 128 Krull's descent lemma 228, 281 Kummer, Eduard (1810|
–1893) 152, 276 Kummer extension 152 Kummer theory 153, 265, 268 Kummer's
Lemma 276 Lagrange resolvent 145 Lagrange, Joseph Louis (1736–1813) 27, ...
|Kummer showed that this set is finite, hence it is a group, called the ideal class |
group. The number of its elements is ... This was another beautiful result of
Kummer, today called Kummer's lemma on units. In his regularity criterion,
|... 552 Krull-Schmidt-Akizuki theorem, 338 Krull topology, 4 Kuga-Sato varieties, |
563 Kummer congruence, 522 Kummer generators, 105 Kummer sequence, 29
Kummer's lemma, 512 Kummer's work on cyclotomic fields, 508–513 L-functions,