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PrimaryDecomposition > localize(Ideal,Ideal)

localize(Ideal,Ideal) -- localize an ideal at a prime ideal

Synopsis

Description

The result is the ideal obtained by first extending to the localized ring and then contracting back to the original ring.
i1 : R = ZZ/(101)[x,y];
i2 : I = ideal (x^2,x*y);

o2 : Ideal of R
i3 : P1 = ideal (x);

o3 : Ideal of R
i4 : localize(I,P1)

o4 = ideal(x)

o4 : Ideal of R
i5 : P2 = ideal (x,y);

o5 : Ideal of R
i6 : localize(I,P2)

             2
o6 = ideal (x , x*y)

o6 : Ideal of R
i7 : R = ZZ/31991[x,y,z];
i8 : I = ideal(x^2,x*z,y*z);

o8 : Ideal of R
i9 : P1 = ideal(x,y);

o9 : Ideal of R
i10 : localize(I,P1)

o10 = ideal (y, x)

o10 : Ideal of R
i11 : P2 = ideal(x,z);

o11 : Ideal of R
i12 : localize(I,P2)

                 2
o12 = ideal (z, x )

o12 : Ideal of R
Author and maintainer: C. Yackel, cyackel@math.indiana.edu. Last modified June 2000.

Caveat

The ideal P is not checked to be prime.

See also