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What is the definition of a characteristic of a ring?

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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.
 

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  • #2
Dick
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What does the definition of 'ring characteristic' say?
 
  • #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.
 
  • #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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