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Strongly multiplicative sets, idempotent localizations, and $S$-prime phenomena
A multiplicative set $S$ of a commutative ring $R$ is strongly multiplicative if every family $(s_i)_{i \in I}$ of elements of $S$ admits a common multiple in $S \cap \bigcap_{i \in I} s_iR$. We combine the structural results on strongly multiplicative sets with their prime-theoretic and module-theo
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