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 March 2nd, 2018, 08:23 AM #1 Senior Member   Joined: Jan 2016 From: Blackpool Posts: 104 Thanks: 2 Ring counter example let R be the set of functions which maps complex numbers to complex numbers. For $f,g\in R$ define functions where $(f+_{R}g)(t)=f(t)+g(t)$ and $(f X_{R}g)(t)=(f \circ g)(t)=f(g(t))$ so that $+_{R}$ is the usual pointwise addition of functions but $X_{R}$ is the composition of functions. Show that R is not a ring with respect to these operations. what would be the easiest way to prove this? By contradicting the ring distributivity laws? Also how would i go about doing this. Thanks Last edited by Jaket1; March 2nd, 2018 at 08:28 AM. March 2nd, 2018, 10:18 AM   #2
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 Originally Posted by Jaket1 what would be the easiest way to prove this? By contradicting the ring distributivity laws? Also how would i go about doing this. Thanks Distributivity is the obvious way to go. Look at some simple examples, it's hard NOT to find a counterexample once you do this. Tags counter, 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 guranbanan Algebra 4 September 19th, 2015 06:36 AM AceCop Probability and Statistics 2 January 15th, 2015 02:19 PM Ganesh Ujwal Topology 0 January 7th, 2015 05:25 AM Modus.Ponens Real Analysis 0 May 16th, 2012 02:57 PM aloria Real Analysis 2 January 25th, 2012 05:20 AM

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