p********e
发帖数: 16048 | 1 f: B -> A ring map
A and B are commutative ring with 1.
M is a B-module.
p is a prime of A. f^{-1}p is then a prime of B.
M_{f^{-1}p} \tensor_B_{f^{-1}p} A_p是否等于 (M\tensor_B A)_p ?
[X_p means the localization of X at p.] |
p********e
发帖数: 16048 | 2 回答这个问题有包子
f: B -> A ring map
A and B are commutative ring with 1.
M is a B-module.
p is a prime of A. f^{-1}p is then a prime of B.
M_{f^{-1}p} \tensor_B_{f^{-1}p} A_p是否等于 (M\tensor_B A)_p ?
[X_p means the localization of X at p.]
【在 p********e 的大作中提到】
: f: B -> A ring map
: A and B are commutative ring with 1.
: M is a B-module.
: p is a prime of A. f^{-1}p is then a prime of B.
: M_{f^{-1}p} \tensor_B_{f^{-1}p} A_p是否等于 (M\tensor_B A)_p ?
: [X_p means the localization of X at p.]
|
H*****s
发帖数: 32 | 3 Yes. There is a canonical isomorphism between them.
Use the fact that N_p=N\otimes_A A_p, for any A module N, and the
associativity:
(M\otimes N)\otimes O=M\otimes(N\otimes O)
【在 p********e 的大作中提到】
: f: B -> A ring map
: A and B are commutative ring with 1.
: M is a B-module.
: p is a prime of A. f^{-1}p is then a prime of B.
: M_{f^{-1}p} \tensor_B_{f^{-1}p} A_p是否等于 (M\tensor_B A)_p ?
: [X_p means the localization of X at p.]
|
