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 Abstract Algebra Abstract Algebra Math Forum

 October 18th, 2011, 09:29 AM #1 Newbie   Joined: Oct 2009 Posts: 14 Thanks: 0 homomorphism, fraction ring Hello, I would really apreciate some help with this... f is a ring homomorphism between two commutative rings A and B. So f: A --->B S is a multiplicatively closed subset of A. Define T:= f(S) then T is a multiplicatively closed subset of B. The book says that there is a homomorphism ,say h, between the ring of fractions S^(-1)B and T^(-1)B which sends b/s to b/f(s). In fact this is an isomorphism. And S^(-1)B and T^(-1)B are isomorphic as S^(-1)A-modules. I already get stuck at this: h((b1/s1) + (b2/s2))= h ((b1s2 + b2s1)/s1s2)= (b1s2 + b2s1)/f(s1s2) = (b1s2)/(f(s1)f(s2)) + (b2s1)/(f(s1)f(s2)) how is this equal to h(b1/s1) + h(b2/s2) can I do this: (b1s2)/(f(s1)f(s2)) = (b1/f(s1)) s2(1/f(s2))= (b1/f(s1)) s2(f(1)/f(s2)) = (b1/f(s1)) (f(s2)/f(s2)) ??? Tags fraction, homomorphism, ring Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post sebaflores Abstract Algebra 3 November 25th, 2013 05:46 AM tiger4 Abstract Algebra 2 April 30th, 2012 03:32 PM tinynerdi Abstract Algebra 3 April 28th, 2010 11:08 AM fermatprime371 Abstract Algebra 2 February 5th, 2009 05:00 PM Erdos32212 Abstract Algebra 0 November 18th, 2008 08:14 PM

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