Let phi: R --> R' be a homomorphism where both R and R' are commutative rings and I is a subring of R. Show that if J is a prime ideal of R' and I = phi^-1(J), then I is a prime ideal of R.

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- Apr 14th 2009, 07:12 PMCoda202Prime Ideals of Commutative Rings
Let phi: R --> R' be a homomorphism where both R and R' are commutative rings and I is a subring of R. Show that if J is a prime ideal of R' and I = phi^-1(J), then I is a prime ideal of R.

- Apr 14th 2009, 07:27 PMNonCommAlg