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Homework Help: Second Abstract Proof

  1. Jul 26, 2010 #1
    Let R be a commutative ring. Show that the characteristic or R[x] is the same as the characteristic of R.

    I'm really not sure where to start on this at all. i'm not sure what is ment by R.
  2. jcsd
  3. Jul 26, 2010 #2


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    R is a commutative ring, they said that. R[x] is the ring of polynomials in x over R. Now at least show some attempt or thought about the problem.
  4. Jul 26, 2010 #3
    I think that there are several typos in your post. Did you mean to state "Show that the characteristic of R[x] is ...". Also, R is the ring in question. Did you mean that you're not sure what is meant by R[x]? If so, R[x] is the ring of polynomials in one variable with coefficients in R. If my assumptions are correct, what is the unit element of R[x]? How does this relate to the definition of the characteristic of the ring?
  5. Jul 26, 2010 #4
    i need to show for that for a polynomial in say, z mod m the characteristic is m, meaning 1+1+1... (n-summations)
  6. Jul 27, 2010 #5


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    No, you don't because you are NOT dealing with "say, z mod m" you are dealing with an abstract commutative ring. What is the DEFINITION of "characteristic" for a commutat9ive ring? What is the definition of "characteristic" for a ring of polynomials with coefficients in a commutative ring?
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