October 30th, 2007, 08:12 AM  #1 
Newbie Joined: Oct 2007 Posts: 7 Thanks: 0  Rings
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.

October 30th, 2007, 10:42 AM  #2 
Site Founder Joined: Nov 2006 From: France Posts: 824 Thanks: 7 
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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