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Abstract algebra help !

  1. Oct 7, 2006 #1
    Abstract algebra help plz!

    I'm not sure if I've posted in the correct forum but I would like some help with the following question:

    http://i12.tinypic.com/33mlik6.jpg

    I've to complete this table but I am unsure of how to do the very first step which is to fnd wv.

    I am learning this from a book and this is one of the given exercises however it doesn't provide a solution so I am really stuck. Hope someone can help!! :frown:

    I know the associative law is:

    a * ( b * c ) = (a * b) * c

    (but I am unsure on how to apply this to my question. Can anyone start me off?)



    thanks very much!
     
  2. jcsd
  3. Oct 7, 2006 #2

    radou

    User Avatar
    Homework Helper

    Well, write down the facts you know from the table, for example w*x = z. Combine all these to obtain the value of w*v. In general, the associative law states that you can insert and delete brackets how you like.
     
  4. Oct 7, 2006 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You want w*v and the hint is to use the associative law: okay, it must be something like w*( ) where the ( ) is a product of two elements that give v: according to your table, what product gives a result of v?
     
  5. Oct 7, 2006 #4
    Okay thanks guys :wink:

    I have got:

    w*v =

    w*(x*y) = w*(x*y)
    = z*y
    = u

    Is that right? So w* v = u?

    The next part of the question is to deduce the identity element so:

    z*y = y*z = z? So the identity element is y? :confused:
     
  6. Oct 9, 2006 #5
    Hi again,

    Could someone help me with this again? Very sorry to be a pain...I'm just so confused :frown:

    I managed to deduce that the identity is u not y as I stated above. And my next step is to fill in the w row and z column but I don't know where to start. For example how can I find w*w?? Do I use the associative law again?

    http://i12.tinypic.com/2guxmz8.jpg


    Thanks in advance!
     
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