1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Polynomials in Z modulus 9

  1. Aug 10, 2008 #1
    I'm trying to figure out how to prove that every polynomial in [itex]\mathbb{Z}_9[/itex] can be written as the product of two polynomials of positive degree (except for the constant polynomials [3] and [6]). This basically is just showing that the only possible irreducible polynomials in [itex]\mathbb{Z}_9[/itex] are the constant ones, [3] and [6], and that all the other constant polynomials can be written as the product of polynomials with degrees greater than 0, kind of like how [1] can be written as,

    [tex]([3]x+[1])([6]x+[1])=[0]x^2+[3]x+[6]x+[1]=[1][/tex]

    but I'm a bit lost on how to show it all, because it's not a field so the theorems I've been studying regarding irreducibility in polynomials don't apply to such a situation. Thanks, any help is greatly appreciated.
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?
Draft saved Draft deleted