The ring R = Q[X,Y] where Q is the rational numbers The ideal I = <X+1> The factor ring is R/I = Q[X,Y]/<X+1> How can i work out whether this factor ring is a field or not?
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Originally Posted by Siknature The ring R = Q[X,Y] where Q is the rational numbers The ideal I = <X+1> The factor ring is R/I = Q[X,Y]/<X+1> How can i work out whether this factor ring is a field or not? Theorem: if R is a unitary commutarive ring and I an ideal in R, R/I is a field iff I is a maximal ideal. So is I= <X+1> maximal? Tonio
Originally Posted by tonio So is I= <X+1> maximal? Tonio No, I=<X+1> is not maximal. But that it is in fact what i was originally trying to prove and i thought i could use the theorem you have stated to do so. What is a better way of proving that I=<X +1> is not maximal?
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