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

- 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}

## See also

- pushFwd(Matrix) -- push forward of a module map via a finite ring map

## Ways to use this method:

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

The source of this document is in /build/macaulay2-88fgJW/macaulay2-1.25.11+ds/M2/Macaulay2/packages/PushForward.m2:381:0.