Timeline for Primes in a (commutative) Jacobson ring
Current License: CC BY-SA 2.5
3 events
| when toggle format | what | by | license | comment | |
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| May 24, 2010 at 11:30 | comment | added | Simon Wadsley | Great! Permit me to rephrase this in algebra rather than geometry for the sake of algebraists. Pick $f$ in the Jacobson radical but non-zero and let $P$ be an ideal that is maximal amongst ideals disjoint from the set of powers of $f$. $P$ is prime but cannot be maximal so is (by condition 2) the intersection of the prime ideals that strictly contain it. But by definition of $P$ all these strictly bigger primes conatin $f$ thus $P$ contains $f$ a contradiction. Nice. | |
| May 24, 2010 at 11:27 | vote | accept | Simon Wadsley | ||
| May 23, 2010 at 7:23 | history | answered | Kevin Ventullo | CC BY-SA 2.5 |