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coApproximationSequence -- Short exact sequence of the MCM coapproximation

Synopsis

Description

The coapproximation sequence of a module M over a Gorenstein ring is the versal short exact sequence $$0\to M \to P \to M' \to 0$$ where M' is a maximal Cohen-Macaulay module and P is a module of finite projective dimension, as defined by Auslander and Buchweitz.

i1 : S = ZZ/101[a,b]/ideal(a^3+b^3)

o1 = S

o1 : QuotientRing
 
i2 : R = S/ideal(a*b)

o2 = R

o2 : QuotientRing
 
i3 : M = R^1/(ideal vars R)^2

o3 = cokernel | a2 0 b2 |

                            1
o3 : R-module, quotient of R
 
i4 : coApproximationSequence M

                                     2
o4 = 0 <-- cokernel {-2} | b2 | <-- R  <-- M <-- 0
                    {-2} | a2 |                   
     0                              2      3     4
           1

o4 : ChainComplex

See also

For the programmer

The object coApproximationSequence is a function closure.