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Allowing 1 to be prime is a lot worse. The integers modulo 1 don't form a field, but modulo a negative prime they do. I think algebraists do generally consider
by ogogmad 6y ago
Allowing 1 to be prime is a lot worse. The integers modulo 1 don't form a field, but modulo a negative prime they do. I think algebraists do generally consider negative primes to be primes.
- pmiller2 6y agoIt's even worse than that. Because integers a and b are congruent modulo n iff n | a - b, and 1 divides every integer, the integers modulo 1 has only 1 element. This gives you the somewhat pathological object called the zero ring: https://en.wikipedia.org/wiki/Zero_ring https://en.wikipedia.org/wiki/Zero_ring