Results 1 to 2 of 2

Thread: [SOLVED] addition and multiplication tables

  1. #1
    Mar 2008

    Lightbulb [SOLVED] addition and multiplication tables

    I have these two Cayley tables. The addition table is complete and the multiplication table is not. The instructions say to use the distributive laws, but I can't seem to find the solutions using the distributive laws. I can only find the solution using the definition of a group.

    Can someone help me?

    ring R = {a, b, c}

    + a b c
    a a b c
    b b c a
    c c a b

    x a b c
    a a a a
    b a c
    c a

    Thanks a bunch!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member TheAbstractionist's Avatar
    Apr 2009
    The additiion table shows that $\displaystyle \langle R+\rangle$ is a group with identity element $\displaystyle a.$ This is the zero element of $\displaystyle R.$

    To complete the table for multiplication, take for example $\displaystyle bc.$ From the addition table, $\displaystyle c=b+b.$ Hence, $\displaystyle bc=b(b+b)=bb+bb=c+c=b.$ (You know $\displaystyle bb=c$ from the partially completed table.)

    Do the same for $\displaystyle cb$ and $\displaystyle cc.$ (Hint: It will turn out that $\displaystyle c$ is the multiplicative identity, and the ring is a field with 3 elements.)
    Last edited by TheAbstractionist; Jun 4th 2009 at 01:20 AM.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Best ways to learn multiplication tables?
    Posted in the Algebra Forum
    Replies: 13
    Last Post: Aug 5th 2012, 11:43 PM
  2. Replies: 2
    Last Post: Apr 22nd 2011, 06:57 PM
  3. Abstract Algebra: Completing coset Multiplication Tables
    Posted in the Advanced Algebra Forum
    Replies: 1
    Last Post: May 4th 2010, 02:41 AM
  4. lim sup and addition, multiplication
    Posted in the Calculus Forum
    Replies: 0
    Last Post: Feb 3rd 2009, 04:05 PM
  5. Replies: 5
    Last Post: Aug 6th 2008, 08:27 AM

Search tags for this page

Click on a term to search for related topics.

Search Tags

/mathhelpforum @mathhelpforum