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Let phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that if T is a subring of R, then the set W= {b S such that b = phi (c) for some c T } is a subring of S. [Be specific of how and where you use that T is a subring of R.]
Show transcribed image text Let phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that if T is a subring of R, then the set W= {b S such that b = phi (c) for some c T } is a subring of S. [Be specific of how and where you use that T is a subring of R.]

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Please help!  Let phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that if T is a subring of R, then the set W= {b S such that b = phi (c) for some c T } is a subring of S. [Be specific of how and where you use that T is a subring of R.] Show transcribed image text Let phi: R rightarrow S be a surjective homomorphism from the ring R to the ring S. Prove that if T is a subring of R, then the set W= {b S such that b = phi (c) for some c T } is a subring of S. [Be specific of how and where you use that T is a subring of R.]

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