Let $M, P, Q$ be prime ideals in a commutative ring $R$ with $P$ properly contained in $M$ and $Q$ disjoint from both $M$ and $P.$ If $A$ is the $R$-module $R/M \oplus R/P \oplus R/Q,$ then the associated primes of $A$ are $M,P,Q.$ In ordinary terminology, $P$ and $Q$ would be called isolated, or minimal primes of $A$. Is there a particular term that I could use to indicate that $Q$ is not contained in another associated prime without writing out "$A$ has an isolated prime that is not properly contained in an associated prime of $A$?" It seems that isolated would be the perfect term, but that is precluded by standard usage. Suggestions would be appreciated.
2026-05-14 11:33:41.1778758421
Is there a special names for associated prime ideals that neither contain nor are contained in other associated primes?
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