Results 1 to 2 of 2

Math Help - Integral Domain

  1. #1
    Junior Member
    Joined
    Sep 2008
    Posts
    26

    Integral Domain

    I am having troubles with the following problem:

    Show that there is an integral domain with exactly 4 elements.

    Any suggestion?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Global Moderator

    Joined
    Nov 2005
    From
    New York City
    Posts
    10,616
    Thanks
    10
    Quote Originally Posted by ynn6871 View Post
    I am having troubles with the following problem:

    Show that there is an integral domain with exactly 4 elements.

    Any suggestion?
    Let F = \mathbb{Z}_2[x] - the polynomials with coefficients in \mathbb{Z}_2.
    Let f(x) = x^2 + x + 1. This polynomial is irreducible over \mathbb{Z}_2[x].
    Therefore, all elements in D=\mathbb{Z}_2[x]/(x^2+x+1) are invertible.
    Consequently, D is an integral domain with |D| = 4.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Integral Domain
    Posted in the Advanced Algebra Forum
    Replies: 9
    Last Post: May 22nd 2011, 12:23 PM
  2. Integral Domain
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 12th 2010, 01:47 AM
  3. Integral domain
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: December 15th 2009, 10:32 AM
  4. Integral Domain
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 15th 2009, 08:33 PM
  5. integral domain?
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: October 23rd 2008, 10:03 AM

Search Tags


/mathhelpforum @mathhelpforum