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Math Help - Operation

  1. #1
    Junior Member
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    Mar 2010
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    Operation

    Hi,

     _* \  is a binary operation in E,

    C is a set defined as:

     C={ y \in E/ (\forall x \in E): y_*x=x_*y }

    I must determine the specifications of (C,_*): associativity, commutativity, neutral element, inverse element...

    I found that _* is commutative but for the others i don't know how to do it.
    Last edited by bhitroofen01; March 24th 2010 at 01:13 PM.
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  2. #2
    Senior Member Tinyboss's Avatar
    Joined
    Jul 2008
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    Quote Originally Posted by bhitroofen01 View Post
    Hi,

     _* \  is a binary operation in E,

    C is a set defined as:

     C={ y \in E/ (\forall x \in E): y_*x=x_*y }

    I must determine the specifications of (C,_*): associativity, commutativity, neutral element, inverse element...

    I found that _* is commutative but for the others i don't know how to do it.
    If E has an identity element (is that what you mean by "neutral element"?) then that identity element commutes with everything in E.

    If * is associative on E, then it's clearly associative on any subset of E.

    If y is in C and x is in E, then y^{-1}x=(x^{-1}y)^{-1}=(yx^{-1})^{-1}=xy^{-1}.
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