Talk:Prime ring

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proof of every boolean ring is a prime ring

Not every Boolean ring is prime, in fact most are not: Boolean rings are commutative, and the only one that's a domain is the field F₂ with two elements. AxelBoldt 15:14, 14 April 2007 (UTC)[reply]

I added the requirement that prime rings be non-zero. In the literature, I often see the characterization "a ring is prime if and only if the zero ideal is a prime ideal"; and this characterization implies that prime rings are non-zero, since prime ideals are proper. AxelBoldt 15:00, 14 April 2007 (UTC)[reply]