Let $R$ be a commutative ring with $1$ such that every minimal prime ideal of $R$ is principal and every minimal prime ideal is contained in either all maximal ideals or in all maximal ideals except one of them, that is, for every minimal prime ideal $p$ of $R$ we have $p\subseteq J(R)$ or there exixts a maximal ideal $m $ of $R$ such that $p\subseteq J(R)-m$. Is there any characterization for such a ring? Or is there any property for such a ring?
2026-03-29 22:38:33.1774823913
Minimal prime ideals contained in the Jacobson radical
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