So I'm new to this concept and when I was reading the definition. It says that if R is a UFD then every non zero element can be written as the product of irreducible elements. So here's my question which is stupid I know. Are these irreducible elements necessarily distinct??
Asked
Active
Viewed 21 times
1 Answers
0
No, the integers are a unique factorization domain and $4=2 \cdot 2$. You have to include the possibility of a unit, which for the integers can only be $-1$, to get the negatives.
Ross Millikan
- 374,822
-
Thanks, now can I say that each element can be written like $p_1^{a_1}....p_n^{a_n}$ where ps are primes?? (It says that irriducable elements are prime elements in UFDs) – Hassuni Nov 26 '20 at 17:19
-
Yes, that is correct if you put in a unit. – Ross Millikan Nov 26 '20 at 20:25