- #1
nadineM
- 8
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I know that Z/(p) that is the integers mod a prime ideal is a field
and I also know that:
Field -> Euclidean Domain -> Principal Ideal domain -> Unique factorization domain ->Domain
So I know that Z/(p) are all of these things.
I also know that Z/(a) That is the set of integers mod a non prime number is not a field. But is it any of the other things? That is it a Euclidean Domain, Principal Ideal domain, Unique factorization domain,Domain, or noetherian?
I have the same question about R[x] and R[x,y] By this notation I mean the sets of polinomials with real coefficients in one and two variable. I believe that R[x] has all of the above listed properties. But I was wondering about R[x,y] I beilve it is not a field but it is noetherian, but I don't know about the other properties...
Can anyone clear these things up? I am just trying to come to a more general understanding of what properties are the same and different in different rings. Thanks
and I also know that:
Field -> Euclidean Domain -> Principal Ideal domain -> Unique factorization domain ->Domain
So I know that Z/(p) are all of these things.
I also know that Z/(a) That is the set of integers mod a non prime number is not a field. But is it any of the other things? That is it a Euclidean Domain, Principal Ideal domain, Unique factorization domain,Domain, or noetherian?
I have the same question about R[x] and R[x,y] By this notation I mean the sets of polinomials with real coefficients in one and two variable. I believe that R[x] has all of the above listed properties. But I was wondering about R[x,y] I beilve it is not a field but it is noetherian, but I don't know about the other properties...
Can anyone clear these things up? I am just trying to come to a more general understanding of what properties are the same and different in different rings. Thanks
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