My Math Forum Ring counter example

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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.

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