Pullback -- pullback in the category of rings

Description

Pullback is a package that implements pullback for diagrams of ringsStart with two maps to a common quotient ring and compute the resulting pullback ring.

i1 : A = QQ[x];

i2 : B = A/ideal(x);

i3 : C = QQ[y];

i4 : f = map(B, A);

o4 : RingMap B <-- A

i5 : g = map(B, C, {0});

o5 : RingMap B <-- C

i6 : R = (pullback(f,g))#0;

i7 : (dim R, numgens ideal R)

o7 = (1, 1)

o7 : Sequence

Caveat

Works only for maps of rings finitely generated over a base field and one of the two maps is surjective

Authors

Drew Ellingson
Karl Schwede

Version

This documentation describes version 1.03 of Pullback, released March 8, 2018.

Citation

If you have used this package in your research, please cite it as follows:

@misc{PullbackSource,
  title = {{Pullback: pullback of rings. Version~1.03}},
  author = {Drew Ellingson and Karl Schwede},
  howpublished = {A \emph{Macaulay2} package available at
    \url{https://github.com/Macaulay2/M2/tree/stable/M2/Macaulay2/packages}}
}

Exports

Functions and commands
- internalUseDirectSum -- Compute direct sum of two rings.
Methods
- internalUseDirectSum(Ring,Ring) -- see internalUseDirectSum -- Compute direct sum of two rings.
- pullback(RingMap,RingMap) -- Compute the pullback of a diagram of rings

For the programmer

The object Pullback is a package, defined in Pullback.m2.

The source of this document is in /build/reproducible-path/macaulay2-1.26.06+ds/M2/Macaulay2/packages/Pullback.m2:411:0.