Let $P,Q$ be ideals such that $P^{2} \subset Q \subset P$ where $\subset$ means proper inclusion and such that $P$ is a prime ideal. Can you please explain why this implies that the ideal $Q$ is never a power of the ideal $P$?
Proper inclusion implies ideal is not power of an ideal
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abstract-algebra
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2Isn't this simply because, for $n>2$, $P^n\subset P^2\subsetneq Q$? – 2011-05-26
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0@Thomas Andrews: doh, right, thanks. – 2011-05-26
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1this holds even if $P$ is not prime. – 2011-05-26