CCE4 Flashcards
1
Q
What is an irreducible element in a ring?
A
An element a is irreducible if:
it is non-zero and not a unit
if a=bc then either b or c is a unit
2
Q
What is a prime element in a ring
A
An element p is prime if
It is non-zero and not a unit
If p divides the product of ab the p divides a or b
3
Q
What is a Principal Ideal Domain (PID)?
A
A PID is an integral domain where every ideal is principal, meaning each ideal I can be written as I=(a) for some a in the domain
4
Q
What is a Unique Factorization Domain (UFD)?
A
A UFD is an integral domain where every non-zero, non-unit element can be uniquely factored into irreducible elements, up to order and units.
