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Math Help - left identity of a set

  1. #1
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    left identity of a set

    Hi,
    I am looking for at least three examples of a set S and and operation * such that there is a left identity and no right identity.
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  2. #2
    MHF Contributor Swlabr's Avatar
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    Quote Originally Posted by htani View Post
    Hi,
    I am looking for at least three examples of a set S and and operation * such that there is a left identity and no right identity.
    Just make some up!

    For instance, let S={a, b} and * be such that

    a*b = b

    b*a = a

    a^2 = a

    b^2 = b.

    This is the right-zero semigroup of order 2. Note that every element is a left identity.

    You should also notice that if S has a right and a left identity then they must be the same element, a `common or garden' identity. So, each of your examples must have a left identity which is not a right identity, which is much easier to verify!

    (This post would have been better suited to the algebra forum...)
    Last edited by Swlabr; March 30th 2010 at 12:46 AM.
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