I would like to know how can I find a ring with (at least) a primary ideal which has n elements (not generators, but elements) for a given n ?
Thank you.
2026-02-23 00:46:09.1771807569
How do I find a ring with a primary ideal having n elements?
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Let $R$ be any ring with $n$ elements and let $S$ be any domain. Then $R\times 0$ is an ideal in the ring $R\times S$ which has $n$ elements, and it is prime since the quotient $R\times S/R\times 0\cong S$ is a domain.