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Unformatted text preview: D1 R , we may extend to a map : D1 R S1 R . Specically if : R D1 R is the natural homomorphism dened by ( r ) = r / 1, then = . All that remains to prove is that is a monomorphism, equivalently ker = 0, so suppose r / d ker where r R and d D . Since ker D1 R , we see that ( r / d )( d / 1 ) = r / 1 ker and hence ( r ) ker . Therefore ( r ) = ( r ) = 0 and since is a monomorphism, we deduce that r = 0. We conclude that r / d = 0 and the result follows....
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 Fall '07
 PALinnell
 Algebra, Fractions

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