|
Author |
Message |
cliomseerg@kriocoucke.mai science forum Guru Wannabe
Joined: 25 Oct 2005
Posts: 128
|
Posted: Tue May 30, 2006 9:18 am Post subject:
Prime ideals of tensor products
|
|
|
Dear NG,
If I have commutative rings and I know their prime ideals, and I know
that I can make a tensor product between them with respect to some ring
(say Z), then can I completely determine the prime ideals in this
tensor product?
Sincerely,
Jose Capco |
|
Back to top |
|
 |
Jannick Asmus science forum Guru
Joined: 25 Mar 2005
Posts: 312
|
Posted: Mon Jun 05, 2006 9:48 pm Post subject:
Re: Prime ideals of tensor products
|
|
|
On 30.05.2006 11:18, Jose Capco wrote:
Quote: | Dear NG,
If I have commutative rings and I know their prime ideals, and I know
that I can make a tensor product between them with respect to some ring
(say Z), then can I completely determine the prime ideals in this
tensor product?
|
I think this is not possible in general. E.g., let R=Z[X] and K be any
field, we have K(x)_Z Z[X] = K[X] and the non-trivial prime ideals in
K[X] are generated by irreducible polynomials which cannot be coded by
any prime ideals in Z[X] and K.
Nevertheless, if R and S are finitely generated algebras over a field k,
then there is a link between the maximal ideals of the tensor product
R(x)S (over k) and the set theoretic product of the maximal spectra of R
and S. This is one of the starting points of the theory of varieties.
Quote: |
Sincerely,
Jose Capco
|
HTH.
Best wishes,
J. |
|
Back to top |
|
 |
Google
|
|
Back to top |
|
 |
|
The time now is Sat Apr 21, 2018 9:39 am | All times are GMT
|
Copyright © 2004-2005 DeniX Solutions SRL
|
Other DeniX Solutions sites:
Electronics forum |
Medicine forum |
Unix/Linux blog |
Unix/Linux documentation |
Unix/Linux forums |
send newsletters
|
|
Powered by phpBB © 2001, 2005 phpBB Group
|
|