# book for help on problems with noetherian rings

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.

• Matsumura "commutative ring theory"? – slider Jun 22 '15 at 19:57
• 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. – Youngsu Jun 22 '15 at 23:12
• Do you see another book which difference to Matsumura ?I want to read a book which it has a hint for this problems.thanks – Albert harold Jun 23 '15 at 8:02
• @ Youngsu: Is this true for every principal ideal of hight one?thank u so much... – Albert harold Jun 23 '15 at 8:10