2 ms·
Not really. Unique factorization is defined up to units, so, factors of +-1 don't matter. 1 is not a prime because it's a unit, and the ideal it generates is
by pmiller2 6y ago
Not really. Unique factorization is defined up to units, so, factors of +-1 don't matter. 1 is not a prime because it's a unit, and the ideal it generates is trivial; it's the entire ring, so, for Z, it's all of Z.
- FartyMcFarter 6y agoThe fundamental theorem of arithmetic doesn't say anything about units though: https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithmetic https://en.wikipedia.org/wiki/Fundamental_theorem_of_arithme... > every integer greater than 1 either is a prime number itself or can be represented as the product of prime numbers and that, moreover, this representation is unique, up to (except for) the order of the factors.
- ogogmad 6y agoLook up the definition of a Unique Factorisation Domain and a prime element of a ring. The theorem that the integers form a UFD necessarily takes into account negative primes. [Edit] Here: https://en.wikipedia.org/wiki/Unique_factorization_domain https://en.wikipedia.org/wiki/Unique_factorization_domain