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JohnKeats

Could someone clarify the notion of a ring with identity element $1=0$? Apparently it's just the zero ring, but then why do we always talk about a ring with identity $1 \ne 0$? It's like having to talk about prime $p \ne 1$; instead we don't define $1$ as a prime but also because we would lose unique factorisation. So what would be lost if we said the zero ring is in fact not a ring?

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