Results 1 to 2 of 2

Math Help - urgent about field

  1. #1
    Newbie
    Joined
    Dec 2008
    Posts
    18

    Exclamation urgent about field

    Let
    R be a ring without identity, and let S = R+Z (+ means addition in sets). On the commutative group S, we define a multiplication by

    (
    r,a).(r,b) = (rr + ar + br,ab)
    for all (r,a), (r,b) are in S. Prove that S is a ring with identity.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    May 2008
    Posts
    2,295
    Thanks
    7
    Quote Originally Posted by bogazichili View Post
    Let


    R be a ring without identity, and let S = R+Z (+ means addition in sets). On the commutative group S, we define a multiplication by

    (r,a).(r,b) = (rr + ar + br,ab)
    for all (r,a), (r,b) are in S. Prove that S is a ring with identity.
    you really ruined the beauty of this problem by putting "urgent" and the unrelated "field" in the title of your post! the idea of embedding a non-unitary ring (as an ideal) in a unitary ring,

    although very simple but it's quite nice and helpful. what you need to notice here is that 1_S=(0,1), \ 0_S=(0,0), \ -(r,a)=(-r,-a). the rest is just checking the axioms.
    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. Splitting Field of a Polynomial over a Finite Field
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: April 1st 2011, 03:45 PM
  3. Field of char p>0 & splitting field
    Posted in the Advanced Algebra Forum
    Replies: 2
    Last Post: April 22nd 2009, 12:20 AM
  4. urgent help about field
    Posted in the Advanced Algebra Forum
    Replies: 3
    Last Post: December 24th 2008, 04:41 PM
  5. URGENT! Find splitting field and roots
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: December 17th 2008, 04:25 PM

Search Tags


/mathhelpforum @mathhelpforum