Question: 1. Let R be a commutative ring and let I C R be an ideal. Define the radical Rad I of I as the set

1. Let R be a commutative ring and let I C R be an ideal. Define the radical Rad I of I as the set RadI = {r R|r" I for some integer n}. (a) Prove that Rad [ is also an ideal of R. (b) Prove that Rad(Rad I) = Rad I. (c) If I = (m) is an ideal in Z, find Rad I, i.e., find an integer n (depending on m) such that Rad I = (n)

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