pushFwd(RingMap,Module) -- push forward of a module via a finite ring map

Synopsis

Function: pushFwd
Usage:

N = pushFwd(f, M)

N = pushFwd M
Inputs:
- f, a ring map, from a ring $A$ to a ring $B$ or the natural map from coefficientRing B if f not specified
- M, a module, a $B$-module, which via $f$ is a finite $A$-module
Optional inputs:
- NoPrune => ..., default value false, NoPrune option for pushFwd
Outputs:
- N, a module,

Description

Given a (not necessarily finite) ring map $f : A \to B$, the $B$-module $M$ can be considered as a module over $A$. If $M$ is finite, this method returns the corresponding $A$-module.

i1 : kk = QQ;

i2 : A = kk[t];

i3 : B = kk[x,y]/(x*y);

i4 : use B;

i5 : i = ideal(x)

o5 = ideal x

o5 : Ideal of B

i6 : f = map(B,A,{x})

o6 = map (B, A, {x})

o6 : RingMap B <--- A

i7 : pushFwd(f,module i)

      1
o7 = A

o7 : A-module, free, degrees {1}

pushFwd(RingMap,Module) -- push forward of a module via a finite ring map

Synopsis

Description

See also