Unformatted text preview: α : R → Z / 2 Z and β : R → Q . Prove that there exists a ring epimorphism θ : R → Z / 2 Z × Q . (2 points) 3. Let R be an integral domain, let S be a multiplicatively closed subset of R which contains 1 but not 0, and let p be a prime of R . Prove that p / 1 is either a prime or a unit of S1 R . (3 points) 4. Exercise 9.4.7 on p. 311 (1 point) (4 problems, 9 points altogether)...
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 Spring '08
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 Math, Algebra, Ring theory, Commutative ring, multiplicatively closed subset

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