|
Books > Science & Mathematics > Mathematics > Algebra > Groups & group theory
|
Buy Now
Classical and Involutive Invariants of Krull Domains (Hardcover, 1999 ed.)
Loot Price: R2,987
Discovery Miles 29 870
|
|
|
Classical and Involutive Invariants of Krull Domains (Hardcover, 1999 ed.)
Series: K-Monographs in Mathematics, 5
Expected to ship within 10 - 15 working days
|
Just suppose, for a moment, that all rings of integers in algebraic
number fields were unique factorization domains, then it would be
fairly easy to produce a proof of Fermat's Last Theorem, fitting,
say, in the margin of this page. Unfortunately however, rings of
integers are not that nice in general, so that, for centuries, math
ematicians had to search for alternative proofs, a quest which
culminated finally in Wiles' marvelous results - but this is
history. The fact remains that modern algebraic number theory
really started off with in vestigating the problem which rings of
integers actually are unique factorization domains. The best
approach to this question is, of course, through the general the
ory of Dedekind rings, using the full power of their class group,
whose vanishing is, by its very definition, equivalent to the
unique factorization property. Using the fact that a Dedekind ring
is essentially just a one-dimensional global version of discrete
valuation rings, one easily verifies that the class group of a
Dedekind ring coincides with its Picard group, thus making it into
a nice, functorial invariant, which may be studied and calculated
through algebraic, geometric and co homological methods. In view of
the success of the use of the class group within the framework of
Dedekind rings, one may wonder whether it may be applied in other
contexts as well. However, for more general rings, even the
definition of the class group itself causes problems."
General
Is the information for this product incomplete, wrong or inappropriate?
Let us know about it.
Does this product have an incorrect or missing image?
Send us a new image.
Is this product missing categories?
Add more categories.
Review This Product
No reviews yet - be the first to create one!
|
You might also like..
|
Welcome to Loot.co.za!
Sign in / Register |Wishlists & Gift Vouchers |Help | Advanced search
