- #1
DanielThrice
- 29
- 0
I'm working on prime an maximal ideals. My partner and I are studying for our final exam and got conflicting answers.
The question was to find all of the prime and maximal ideals of [tex]\mathbb Z_7[/tex]. My answer was that because a finite integral domain is a field, the prime and maximal ideals coincide, but that there are no prime and maximal ideals for [tex]\mathbb Z_7[/tex].
As for [tex]\mathbb Z_3 \times \mathbb Z_5[/tex], what are the prime and maximal ideals, and more importantly, how in the world do we know that we have found them all?
The question was to find all of the prime and maximal ideals of [tex]\mathbb Z_7[/tex]. My answer was that because a finite integral domain is a field, the prime and maximal ideals coincide, but that there are no prime and maximal ideals for [tex]\mathbb Z_7[/tex].
As for [tex]\mathbb Z_3 \times \mathbb Z_5[/tex], what are the prime and maximal ideals, and more importantly, how in the world do we know that we have found them all?