 About 10,300 results  books.google.com 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 ... 

 books.google.com 
 books.google.com 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
let ... 

 books.google.com (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
celebrated ... 

 books.google.com Kummer's proof follows the outline of the proof of Theorem 32.6; 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 ... 

 books.google.com 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. 

 books.google.com 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
paper ... 

 books.google.com ... 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, ... 

 books.google.com 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,
Kummer ... 

 books.google.com ... 552 KrullSchmidtAkizuki theorem, 338 Krull topology, 4 KugaSato varieties,
563 Kummer congruence, 522 Kummer generators, 105 Kummer sequence, 29
Kummer's lemma, 512 Kummer's work on cyclotomic fields, 508–513 Lfunctions,
... 

 