Hint: Let A be the set of zero divisors and B the set of units then
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 .