computing an intersection of submodules over different rings

[Avi Steiner]

Let f : R -> S be a map of rings. Let M be an S-module, N an R-module, and g : N-> M a map of R-modules (with respect to f). Let L be an S-submodule of M. How do I compute a generating set for g^-1(L)?

For concreteness, here's an explicit setup in M2 code:

R = QQ[m_0..m_2]
S = QQ[x,y,z,a,b,c]
f = map(S, R, {y*c-z*b, -x*c+z*a, x*b-y*a})
M = S^1
N = R^{3:-1}
g = map(M, N, f, {{x,y,z}})
L = module ideal (x,y,z)

Best,

Avi

[jche...@gmail.com]

Hi Avi,

What about computing the kernel of g, after replacing M with M/L? (E.g. "gens ker map(M/L, N, f, {{x,y,z}})" in your example.)

Justin

[Avi Steiner]

Thanks! That works! :)