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Math Help - Tensorial Product

  1. #1
    Newbie
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    Sep 2010
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    Post Tensorial Product

    Hi,
    I have to solve this question, I appreciate your help.
    The ring \mathbb{C} \otimes_{\mathbb{R}} \mathbb{C} isn't an Integral Domain
    The multiplication operation in this ring is the usual complex multiplication by components.

    Thanks
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  2. #2
    MHF Contributor

    Joined
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    Thanks
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    let x = 1 \otimes i - i \otimes 1 and y = 1 \otimes i + i \otimes 1. what is xy? note that both x and y are non-zero because  \{1,i\} is linearly independent over \mathbb{R}.

    by the way, you can find your example and a better one in here. that's my blog!
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