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Results tagged with prime-ideals
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user 17218
For questions involving prime ideals in commutative or noncommutative rings.
6
votes
1
answer
557
views
prime ideals minimal over a zerodivisor
Let $R$ be a commutative ring with identity. If $P$ is a prime ideal of $R$ that is minimal over some zerodivisor of $R$, then must $P$ consist only of zerodivisors? I suspect not but I can't figure …
- 4,985
3
votes
Intersection of powers of prime ideals
No reference, but the proof is trivial. If $ab = 0$, then $x^{2n} | ab$ (for any $n$), so since $x$ is prime and a nonzerodivisor, $x^n | a$ or $x^n | b$, and since this is true for all $n$, either …
- 4,985