Let $R$ be a commutative ring with unit. Is it true that given an ideal $I$ and $r \geq 2$ principal ideals $P_1, ..., P_r$, then if $I \subseteq \bigcup_{i = 1}^r P_i$, $I \subseteq P_i$ for some $i$? This would be the analogous of the Prime Avoidance Lemma for principal ideals.
2026-04-01 08:00:40.1775030440
Principal Ideal Avoidance
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