I'm struggling on the basic verification that in a commutative ring with only one prime ideal $P$, all elements are units or nilpotent. I have all the facts in front of me: The nilradical is just $P$, which is also the Jacobson radical, and if $x \notin P$, then $P + (x) = (1)$--but I can't figure out how to put them together. How do I conclude that $x$ is a unit from this?
2026-03-28 15:26:45.1774711605
All Elements are Units or Nilpotent in a Ring with a Unique Prime Ideal
132 Views Asked by Bumbble Comm https://math.techqa.club/user/bumbble-comm/detail AtRelated Questions in COMMUTATIVE-ALGEBRA
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