Results 1 to 3 of 3

Math Help - How to work out whether this factor ring is a field or not

  1. #1
    Junior Member
    Joined
    Oct 2009
    Posts
    39

    How to work out whether this factor ring is a field or not

    The ring R = Q[X,Y] where Q is the rational numbers

    The ideal I = <X+1>

    The factor ring is R/I = Q[X,Y]/<X+1>

    How can i work out whether this factor ring is a field or not?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Banned
    Joined
    Oct 2009
    Posts
    4,261
    Thanks
    2
    Quote Originally Posted by Siknature View Post
    The ring R = Q[X,Y] where Q is the rational numbers

    The ideal I = <X+1>

    The factor ring is R/I = Q[X,Y]/<X+1>

    How can i work out whether this factor ring is a field or not?

    Theorem: if R is a unitary commutarive ring and I an ideal in R, R/I is a field iff I is a maximal ideal.

    So is I= <X+1> maximal?

    Tonio
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2009
    Posts
    39
    Quote Originally Posted by tonio View Post
    So is I= <X+1> maximal?

    Tonio
    No, I=<X+1> is not maximal.

    But that it is in fact what i was originally trying to prove and i thought i could use the theorem you have stated to do so.

    What is a better way of proving that I=<X +1> is not maximal?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Ring, field, Galois-Field, Vector Space
    Posted in the Advanced Algebra Forum
    Replies: 4
    Last Post: November 15th 2012, 03:25 PM
  2. ring and field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: March 5th 2011, 06:00 AM
  3. Factor ring
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 14th 2009, 11:16 AM
  4. ring -> field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: January 3rd 2009, 06:38 PM
  5. Field problem with factor ring
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: November 13th 2007, 06:41 PM

Search Tags


/mathhelpforum @mathhelpforum