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October 30th, 2007, 08:12 AM   #1
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Let R be the collection of all functions f(x) from the reals to the reals; this is a ring under pointwise addition and multiplication of functions. Define a subset S to consist of all those functions h(x) for which h(2) = 2h(1). Determine whether S is or is not a subring of R.
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October 30th, 2007, 10:42 AM   #2
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It's not, because whenever you take j and k two functions belonging to this collection, you have (j * k)(2)=j(2)*k(2)=2*j(1)*2*k(1)=4*(j*k)(1), which is in general different from 2*(j*k)(1).
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