No, I have never heard of that theorem.
My confusion comes from this phrase: "...which determine the zero function...". Determine in what sense, and the zero function on which domain? These are two unknowns which can change the question completely, I cannot keep guessing what they mean. If you know what they mean, please elaborate. Otherwise, you should clarify with your instructor/book.
I only have two more problems in this chapter then I can move on to the next chapter. I hope that the next chapter is better than this one. Well I have to go to work tomorrow!! Thanks for trying to help if you figure it out that would be great
I just took a look at your book, and it seemed we can just substitute elements of whenever we want. In this case, our job is quite easy actually. To see that
is an ideal, we want to show that it is closed under addition by elements in and closed under multiplication by elements of . For the first bit, suppose . Then for all . Thus . For the second assertion, suppose . Then for all . Therefore .