# Ideals over K[x,y]

• Nov 7th 2008, 07:05 PM
roporte
Ideals over K[x,y]
Prove the equality between ideals in K[x,y]:

$=$

thanks!
• Nov 7th 2008, 08:16 PM
NonCommAlg
Quote:

Originally Posted by roporte
Prove the equality between ideals in K[x,y]:

$=$

thanks!

call the ideals in the LHS and RHS $I$ and $J$ respectively. clearly $I \subseteq J.$ so we only need to show that $x \in I$ and $y \in J$:

$x=x+xy + x^2y - x(y+xy) \in J, \ \ y=y+xy + y^2x - y(x+xy) \in J. \ \ \ \Box$