# Math Help - Zero Function

1. ## Re: Zero Function

No, I have never heard of that theorem.

2. ## Re: Zero Function

In that case, I don't think my interpretation of your question is correct. Is there any other information you can give me? i.e What topics are you working on right now, or where does the question comes from?

3. ## Re: Zero Function

I just learned/read the Eisenstein Irreducibility Criterion

4. ## Re: Zero Function

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.

5. ## Re: Zero Function

That is why I am here. I dont have an instructor and the book just started putting this term in with no explanation in this chapter

6. ## Re: Zero Function

I have found so many mistakes in this chapter. It makes learning this chapter that much harder. Sorry

7. ## Re: Zero Function

Which book is this?

8. ## Re: Zero Function

A book of Abstract Algebra by Pinter. I think I have gotten to the point where I just dont trust any of the problems

9. ## Re: Zero Function

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

10. ## Re: Zero Function

You're in luck, I found this book in my university library. My original interpretation is correct, and the proof basically amounts to a proof of the theorem I've stated. I will write it down later tonight when I have more time.

11. ## Re: Zero Function

Oh my that would be great!!!! Thanks

12. ## Re: Zero Function

I just took a look at your book, and it seemed we can just substitute elements of $F$ whenever we want. In this case, our job is quite easy actually. To see that

$\mathcal{S}=\{p(x)\in F[x]|p(a)=0 \quad \forall a\in F\}$

is an ideal, we want to show that it is closed under addition by elements in $\mathcal{S}$ and closed under multiplication by elements of $F[x]$. For the first bit, suppose $p(x),q(x)\in \mathcal{S}$. Then $(p+q)(a)=p(a)+q(a)=0+0=0$ for all $a\in F$. Thus $(p+q)(x)\in \mathcal{S}$. For the second assertion, suppose $p(x)\in \mathcal{S},r(x)\in F[x]$. Then $r(a)p(a)=r(a)\cdot 0 = 0$ for all $a\in F$. Therefore $r(x)p(x)\in \mathcal{S}$.

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