2 ms·
> Does this really require knowing abstract algebra? Seems obvious to anyone doing any sort of multiplication that if the output is 0 then one of variables/func
by wz1000 9y ago
> Does this really require knowing abstract algebra? Seems obvious to anyone doing any sort of multiplication that if the output is 0 then one of variables/functions has to be 0
No, this is only true when you are doing multiplication in an integral domain.
https://en.wikipedia.org/wiki/Integral_domain https://en.wikipedia.org/wiki/Integral_domain
There are many rings where this is not true, like Z/nZ where n is not prime.
2*2 = 0 (mod 4)
2 /= 0 (mod 4)
- posterboy 9y agomod should be part of the signature of the ring, so you are not looking at pure multiplication. Then the domain would be still integral. Why wouldn't it?
- opportune 9y agoAn integral domain is any commutative ring with no zero divisors (a,b are zero divisors if ab = 0 but a != 0, b != 0). In this case 2*2 = 0, so 2 is a zero divisor, so Z/4z = Z_4 is not an integral domain.