Are there any rings without unity which can be expressed as a union of its three proper ideals?
2026-03-25 12:53:39.1774443219
Is there a ring without unity which can be expressed as a union of its three proper ideals?
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If your rings are unital, then the answer is no, since $1\in R$ will then be contained in a proper ideal. If you do not insist on a unit, take $R=\mathbb Z_2\times \mathbb Z_2$ with zero multiplication. Then $I_1=\{(0,0),(1,0)\}$, $I_2=\{(0,0),(0,1)\}$, and $I_3=\{(0,0),(1,1)\}$ will work.