Assignment:
Let R be the set of all continuous functions from the set of real numbers into itself. Then R is a commutative ring with the following operations: (f+g)(x)=f(x) + g(x) and (fg)(x)=f(x)g(x) for all x.
Now let I be the set of all functions f(x) an element of R such that f(1)=0. Show that I is a maximal ideal of R.
Maximal ideal: I is a maximal ideal if for all ideals J of R such that I is contained in J is contained in R, then either J=I or J=R. In other words we cannot "squeeze" another ideal between I and the whole ring R.
Provide complete and step by step solution for the question and show calculations and use formulas.