Page 2 of 2 FirstFirst 12
Results 16 to 27 of 27

Math Help - Zero Function

  1. #16
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    Re: Zero Function

    No, I have never heard of that theorem.
    Follow Math Help Forum on Facebook and Google+

  2. #17
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87

    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?
    Follow Math Help Forum on Facebook and Google+

  3. #18
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    Re: Zero Function

    I just learned/read the Eisenstein Irreducibility Criterion
    Follow Math Help Forum on Facebook and Google+

  4. #19
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87

    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.
    Follow Math Help Forum on Facebook and Google+

  5. #20
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    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
    Follow Math Help Forum on Facebook and Google+

  6. #21
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    Re: Zero Function

    I have found so many mistakes in this chapter. It makes learning this chapter that much harder. Sorry
    Follow Math Help Forum on Facebook and Google+

  7. #22
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87

    Re: Zero Function

    Which book is this?
    Follow Math Help Forum on Facebook and Google+

  8. #23
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    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
    Follow Math Help Forum on Facebook and Google+

  9. #24
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    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
    Follow Math Help Forum on Facebook and Google+

  10. #25
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87

    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.
    Follow Math Help Forum on Facebook and Google+

  11. #26
    Newbie
    Joined
    Nov 2012
    From
    USA
    Posts
    22

    Re: Zero Function

    Oh my that would be great!!!! Thanks
    Follow Math Help Forum on Facebook and Google+

  12. #27
    Super Member
    Joined
    Jan 2008
    Posts
    588
    Thanks
    87

    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}.
    Follow Math Help Forum on Facebook and Google+

Page 2 of 2 FirstFirst 12

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: March 16th 2013, 01:38 AM
  2. Replies: 20
    Last Post: November 27th 2012, 06:28 AM
  3. Replies: 0
    Last Post: October 19th 2011, 05:49 AM
  4. Replies: 4
    Last Post: October 27th 2010, 06:41 AM
  5. Replies: 3
    Last Post: September 14th 2010, 03:46 PM

Search Tags


/mathhelpforum @mathhelpforum