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ICmap -- natural map from an affine domain into its integral closure.

Synopsis

Usage:
ICmap R
Inputs:
- R, a ring that is an affine domain
Outputs:
- a ring map from R to its integral closure

Description

Note that if an integrally closed ring is given as input, the identity map from the ring to itself is returned.

i1 : R = QQ[x,y,z]/ideal(x^6-z^6-y^2*z^4);

i2 : ICmap R

                      QQ [w , w , x, y, z]
                           7   6
o2 = map(---------------------------------------------,R,{x, y, z})
           2                    2         2    2    2
         (x  - w z, w x - w z, w  - w x, w  - y  - z )
                6    6     7    6    7    7

                          QQ [w , w , x, y, z]
                               7   6
o2 : RingMap --------------------------------------------- <--- R
               2                    2         2    2    2
             (x  - w z, w x - w z, w  - w x, w  - y  - z )
                    6    6     7    6    7    7

This finite map is needed to compute the conductor of the integral closure into the original ring.

See also

conductor -- compute the conductor of a finite ring map

Ways to use `ICmap` :

ICmap(Ring)