I am a math student, in the course of abstract algebra we have shown that in a unitary commutative ring every ideal I possesses at least one minimal prime ideal. I am trying to find an example of ideal contents in a non-commutative (not unitary) ring that does not possess a minimal prime ideal.
2026-03-28 13:40:16.1774705216
Example of a ring with no minimal prime ideal
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$2\mathbb Z/4\mathbb Z$ does not have any prime ideals.
If you want an $R$ such that $R^2\neq 0$, then $2\mathbb Z/8\mathbb Z$.