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Unformatted text preview: (4) If R is a commutative ring with 1 and x 1 , x 2 are distinct indeterminantes show that R [ x 1 ,x 2 ] and R [ x 1 ] R R [ x 2 ] are isomorphic as Ralgebras. (5) Suppose A is a nitely generated abelian group. (a) Compute A Z Q . (b) Dene f : A A Z Q by setting f ( a ) = a 1 for all a A . Show that f is a homomorphism. Under what circumstances if f a monomorphism? (6) If A is an abelian group show that Z n Z A = A/nA . (7) If K M N 0 is an exact sequence of left Rmodules and L is a right Rmodule show that L R K L R M L R N 0 is an exact sequence of abelian groups....
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 Fall '08
 Staff
 Algebra

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