/sci/ - Science & Math

What is a harsh truth that the scientific community needs to embrace?

I would prefer if we didn't turn this thread into another autism race realism hurricane, please; but if you can discuss it without blowing a gasket then go ahead.

Im doing this proof where every prime element in an integral domain R is irreducible.

Proof: Let p=ab. Then p|a or p|b. wlog p|a. Then a=px. and so we have p=pxb. Integral domain means we can cancel and so xb=1. this means b was a unit.

Im confused by the definition of irreducibility. Is something irreducible if its only divisors are u, ua where u is a unit? So is it isufficient to show that there is a unit present in the factorization above? Im confused because our prof said that EVERY factorization has to be trivial.