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If A={x/x^2= -1, x ∈ R}, then n(p(A)) ...plz give the answer i will mark the correct answer as brainliest. plz don't copy the answers from google or any other browser. |
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Answer» Answer: Let d∈Z be a SQUARE FREE INTEGER. R=Z[d−−√] ={a+bd−−√|a,b∈Z}. Overall, I'm trying to SHOW that every prime ideal P⊂R is a maximal ideal. So far I showed that I⊂R is finitely generated. I={(x,s+yd−−√)} And now I'm trying to show that R/P, for some prime ideal is a finite ring with no zero DIVISORS. From there it would follow that R/P is a field and any prime ideal is maximal. I know R could also be written as R=Z[x]/(x2−d). How could I show that R/P is a quotient of Z/nZ[x]/(x2−d)? |
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