In my book it says that a Ring R can be imbedded in a ring R1 if there is an isomorphism of R onto R1 and we call R1 the over-ring. Some of the things that the author goes on to talk about makes me think that R can just be fit into R1 almost like it's a subset (which I know it's not) of R1. What I'm wondering is that if R is isomorphic to R1 then isn't R1 isomorphic to R so if R can be imbedded in R1 then R1 can be imbedded into R? Can anyone help to make this a little clearer to me?(adsbygoogle = window.adsbygoogle || []).push({});

Another question I had has to do with polynomial rings. If you're trying to show that a certain polynomial is irreducible over a field F[x] is to show that the ideal A = (p(x)) in F[x] is a maximal ideal? What exactly does an ideal (p(x)) in F[x] look like? An example practice problem I have is show that x^3-9 is irreducible over the integers mod31. So I need to show that the ideal (x^3-9 ) is a maximal ideal. what does an ideal of this form look like. maybe not just this example but in general. Also, where does the -9 come in since the integers mod31 are {0,1,2,........,30} which are all positive.

thanks for any help

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# Algebra question

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