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Math Help - Units of Ring

  1. #1
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    Units of Ring

    New to the board and neep help:

    Find the units of the ring R when R is
    (i) Z x Z
    (ii) F(e), where F is a field and e^2=0.
    (iii) M2(F), where F is a field and M2 is a two-by-two matrix.

    Thank you.
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  2. #2
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    Quote Originally Posted by SultanOfSwing View Post
    New to the board and neep help:

    Find the units of the ring R when R is
    (i) Z x Z
    The units in \mathbb{Z} are -1,1
    Thus,
    (-1,1),(-1,-1),(1,-1),(1,1)
    (ii) F(e), where F is a field and e^2=0.
    This is called a trivial ring, or the ring where 1=0
    The additive element is the only unit.

    Unless the notion F(e) means something else?
    (It cannot possibly means a simple extension).
    (iii) M2(F), where F is a field and M2 is a two-by-two matrix.
    All invertible matrices, that is,
    \det (A)\not = 0
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