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What is the definition of a characteristic of a ring?

  1. Mar 28, 2007 #1
    What is the definition of a characteristic of a ring?

    Is it the smallest n such that n1=0? or is it the smallest n such that nr=0 for all r in R.
     
  2. jcsd
  3. Mar 28, 2007 #2

    Dick

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    What does the definition of 'ring characteristic' say?
     
  4. Mar 28, 2007 #3

    HallsofIvy

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    Copied from Wikipedia:

    In mathematics, the characteristic of a ring R with multiplicative identity element 1R is defined to be the smallest positive integer n such that

    n1R = 0,
    where n1R is defined as

    1R + ... + 1R with n summands.
     
  5. Mar 28, 2007 #4

    matt grime

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    Exercise for the reader: show that the two definitions given are equivalent (in a unital ring).
     
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