Can you please introduce to me a book which would help me to prove the two following problems?

  1. In a noetherian ring, every integrally closed ideal is unmixed.

  2. Let $R$ be a noetherian ring, $P$ a prime ideal and $q$ a $P$-primary ideal. Show that $q$ is integrally closed if and only if $qR_{P}$ is.

  • 1
    $\begingroup$ Matsumura "commutative ring theory"? $\endgroup$ – slider Jun 22 '15 at 19:57
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    $\begingroup$ I think 1. is false unless you have a different definition of "unmixed". Take $I = (x^2,xy)$ in a polynomial ring $k[x,y]$, where $k$ is a field. $\endgroup$ – Youngsu Jun 22 '15 at 23:12
  • $\begingroup$ Do you see another book which difference to Matsumura ?I want to read a book which it has a hint for this problems.thanks $\endgroup$ – Albert harold Jun 23 '15 at 8:02
  • $\begingroup$ @ Youngsu: Is this true for every principal ideal of hight one?thank u so much... $\endgroup$ – Albert harold Jun 23 '15 at 8:10

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