Unformatted text preview: x be a nonnilpotent element of R ( y is nilpotent means y n = 0 for some positive integer n ). (a) Prove that there is an ideal P of R maximal with respect to the property x n / ∈ P for all n ∈ Z + . (b) Prove that P is a prime ideal of R . (3 points) (5 problems, 12 points altogether)...
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 Fall '07
 PALinnell
 Math, Algebra, Ring, Prime number, Ring theory

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