Unformatted text preview: u is an element of R satisfying u 2 = 1, show that u = ± 1. [Note: You may not assume that R = Z m .] (c) Why doesn’t (b) contradict (a)? 5 (15 points) . Let R be the set of all complex numbers of the form a + bi , where a and b are rational numbers. (a) Show that R is closed under the usual addition and multiplication operations. (b) Explain why R is a ring. [Hint: This doesn’t require a long answer.] 6 (5 points) . Does there exist a homomorphism Z 2 → Z ? If so, exhibit one. If not, explain why not....
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 Spring '08
 BILLERA
 Math, Algebra, Ring, Prime number

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