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Early Abstract Algebra Problem - Pinter's Textbook

  1. Aug 11, 2012 #1
    1. The problem statement, all variables and given/known data
    This problem is from Charles C. Pinter's A Book of Abstract Algebra, Second Edition. The problem is B7 of Chapter 2.


    Show that the operation * is either associative or not.

    x*y=[itex]\frac{xy}{x+y+1}[/itex]





    This problem seems simple to me: I keep arriving at YES for an answer; more specifically,

    x*(y*z)=(x*y)*z=[itex]\frac{xyz}{xy+xz+yz+x+y+z+1}[/itex].

    However, the solution in the back claims that the answer is NO, the operation is not associative. More specifically,

    x*(y*z)=[itex]\frac{xyz(y+z+1)}{xy+xz+yz+x+y+z+1}[/itex].

    (x*y)*z= [itex]\frac{xyz(x+y+1)}{xy+xz+yz+x+y+z+1}[/itex].

    After working the problem through several times, I'm pretty sure this is a mistake in the book. But I would greatly appreciate feedback so that I can be sure I'm not doing something terribly wrong.

    Thank you very much.
     
  2. jcsd
  3. Aug 11, 2012 #2

    micromass

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    I agree with you. The operation seems to be associative.
     
  4. Sep 19, 2012 #3
    I also get the same result.
     
  5. Sep 19, 2012 #4

    HallsofIvy

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    But surely your text does not "Show that the operation * is either associative or not."
    Every operation is "either associative or not"!

    Better wording would be "Determine whether the operation * is either associative or not."
     
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