Let R be the ring of all real-valued functions defined on the real line.
(a) Find all the zero-divisors in R.
(b) Find all the units in R.
Can someone please help me out a bit, thanks.
Of course, "units" are precisely those members that have multiplicative inverses and the "zero divisors" those that do not.
Of course, the real valued functions form a ring with two different kinds of "multiplication"- f(x)g(x) and f(g(x)). Which do you mean?
Most probably he means the first one since the second one isn't, in a strict fashion, a ring
since functions composition may not yield a function defined in the WHOLE real numbers.
For example, the functions are defined on the real line, but is only defined
in the half line .
Tonio
Not really, in 2 is not a unit or a zero divisor, which is why I gave the fact that in this case it is true as a hint.
Isn't one of them the identity? I don't see how the composition is only defined there. Besides it's easier to see that composition fails to distribute over the sum when the functions involved are non-linear.For example, the functions are defined on the real line, but is only defined
in the half line .