5

How to find a primary decomposition of the ideal $I = (X^2, XY, XZ, YZ)$ in the ring $k[X,Y,Z]$? Is there a general rule for finding primary decompositions?

Also how to show that $(X,Y)^{308}$ is a primary ideal in $k[X,Y,Z]$?

user26857
  • 53,190
user1212
  • 51
  • 1
  • 1
    For monomial ideals there is an algorithm for finding their primary decomposition. For the second use search on this site. (It is obviously primary in $K[X,Y]$ and I proved somewhere that polynomial extensions preserve primality.) –  Apr 03 '13 at 00:35
  • 1
    @YACP The restriction to monomial ideals is not necessary. There are algorithms that compute primary decompositions of ideals in polynomial rings. – Thomas Oct 27 '13 at 16:30
  • see my answer to this question: http://math.stackexchange.com/questions/834673/primary-decomposition-of-i-x2-y2-xy/834687#834687 –  Jul 04 '14 at 11:47

0 Answers0