Let $a$ be a non-unit in a ring $R$. Show that $a$ lies in a maximal ideal.
Is there a way to solve this without using Zorn's Lemma?
2026-04-06 01:58:16.1775440696
Let $a$ be a non-unit in a ring $R$. Show that $a$ lies in a maximal ideal.
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No; without Zorn's lemma, a ring may not have any maximal ideal. See Zorn's lemma in abstract algebra?.