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3 questions with no upvoted or accepted answers
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Quick proof of the first part of Kaplansky's Theorem on characterization of Noetherian domains with all maximal ideals principal
I have been reading section 12 of this paper "Elementary Divisors and Modules" by I. Kaplansky (https://www.ams.org/journals/tran/1949-066-02/S0002-9947-1949-0031470-3/S0002-9947-1949-...
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Properties preserved in addition of ideals
If I and J are prime (radical) ideals then what are the conditions under which we can define a prime (radical) ideal from I+J?
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Intersection of all positive powers of prime ideal in an integral domain with all ideals of finite height
Let $R$ be an integral domain with every prime ideal having finite height. Then is $\bigcap_{n>1} P^n$ a prime ideal of $R$ for every prime ideal $P$ of $R$ ? If that is not true in general, then ...
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