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What is this ring called?

  1. Jun 15, 2007 #1
    This set of four matrices:

    1 0 | 0 1 | -1 0 | 0 1
    0 1 | 1 0 | 0 1 | -1 0

    are closed under multiplication. What is it called? I know that it is not
    those silly quaternions
     
  2. jcsd
  3. Jun 15, 2007 #2

    NateTG

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    Is it the Klein 4-group?
    http://en.wikipedia.org/wiki/Klein_four-group
     
  4. Jun 15, 2007 #3
    Thanks, NateTG, for taking the time to respond. That is what I thought until I realized that it had to be a RING for closure. So then I thought I would like to know the NAME of it, at least.
     
  5. Jun 15, 2007 #4

    NateTG

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    If it's a ring, where's zero, and what are the addition and multiplication operations?
     
  6. Jun 15, 2007 #5
    NateTG,

    0 is just

    0 0
    0 0

    and + is just matrix addition and x is just matrix multiplication.

    I found some stupid wikipedia thing where these 4 were given names like
    K0 K1 K2 K3 but no references were given so that was a dead end.

    I'm at work so I can't look it up in my books.
     
  7. Jun 15, 2007 #6
    Your set is not closed under addition, and thus not a ring.
     
  8. Jun 15, 2007 #7
    repeat after me ... "I don't know" ... all together now ... "I don't know"....
     
  9. Jun 15, 2007 #8

    NateTG

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    So, you mean the ring *generated* by those four elements?
     
  10. Jun 15, 2007 #9
    I don't know... what you're trying to say, or what your question is if you have one.
     
  11. Jun 15, 2007 #10
    ... but name is not so important ... as long as you don't intend to lookup an index ...
     
  12. Jun 15, 2007 #11
    he means multiplication group of course instead of ring
     
  13. Jun 15, 2007 #12

    Office_Shredder

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    The last one squared isn't a member of the group. if it was
    0 -1
    -1 0

    then you'd have the klein 4 group (well, isomorphic to it)
     
  14. Jun 19, 2007 #13

    matt grime

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    1) it isn't a ring
    2) it isn't closed under multiplication.
    3) assuming you really mean 'what is the ring generated by R-linear combinations of these elements' (and that you're operating over R), those elements generate all od M_2(R) the 2x2 matrix ring
     
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