Talk:Primary ideal

I know the proof that

if the radical of Q is maximal, then Q is primary.

I don't have the reference to confirm this, so I'm putting it for now. (Otherwise, I will forget.) -- Taku (talk) 00:10, 23 February 2009 (UTC)

The link to primal is incorrect, it point to algebraic geometry definition of primal, which is out of context. —Preceding unsigned comment added by 85.250.203.213 (talk) 06:45, 30 May 2010 (UTC)

Why bother with radical?

Is it the case that for every primary ideal I, if xy is in I, either x^2 or y^2 is? This is clearly the case for primary ideals in Z. 130.132.173.59 (talk) 15:15, 12 September 2018 (UTC)

Your proposition is trivially false for $x=X$ and $y=Y$ for the primary ideal $(X^{3},Y^{3},XY)$ in the ring $\mathbb {Q} [X,Y]$. Rschwieb (talk) 16:53, 12 September 2018 (UTC)