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!

[Abstract Algebra] Maximal Ideal

  1. Feb 26, 2013 #1
    1. The problem statement, all variables and given/known data
    Let F be the field and f(x)=x-1,g(x)=x^2-1 and F[x]/(f(x)) is isomorphism to F, is it g(x) maximal??


    2. The attempt at a solution

    I will say no.Since g(x) is not 0, the dieal (x^2-1) in a prime idea domain F is maximal iff (x^2-1) is irreducible.
    And we say (x^2-1) is irreducible if it is not a unit, but x^2-1=(x+1)(x-1) implies that either (x+1) or (x-1) is a unit.
    but I can find a taylor expansion of 1/(x^2-1) which means (x^2-1) is a unit, contradicts irreducible

    is my idea right ???
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?



Similar Discussions: [Abstract Algebra] Maximal Ideal
  1. Abstract Algebra (Replies: 0)

Loading...