Unformatted text preview: θ to an Rmap φ : P → M ; speciﬁcally αφ = θβ . Also show by example that the hypothesis P projective cannot be dropped. 6. Let R be a ring with a 1 and let e be an idempotent of R (that means e 2 = e ). Prove that Re is a projective Rmodule. 7. Let R be a ring with a 1 and let Q be an injective left Rmodule. Suppose x ∈ R is not a right zero divisor, that is rx 6 = 0 whenever 0 6 = r ∈ R . Prove that xQ = Q . Exam on Tuesday December 13, 10:05 a.m.–12:05 p.m. in the regular classroom McBryde 202. One of the problems will be identical to one of the ungraded homework problems or sample ﬁnal problems since the second test....
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 Fall '07
 PALinnell
 Math, Algebra

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