I know that(adsbygoogle = window.adsbygoogle || []).push({}); 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 thatZ/(p) are all of these things.

I also know thatZ/(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 aboutR[x] andR[x,y] By this notation I mean the sets of polinomials with real coefficients in one and two variable. I believe thatR[x] has all of the above listed properties. But I was wondering aboutR[x,y] I beilve it is not a field but it is noetherian, but I dont know about the other properties.....

Can any one 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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# Random Ring theory Questions

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