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Homework Help: Proof Help =)

  1. Sep 21, 2010 #1

    silvermane

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    Gold Member

    1. The problem statement:

    Let R be a commutative ring, and suppose b is a zero divisor in R. Let c e any element in R. Prove that the equation bx = c can never have a single solution in R.
    (meaning that if it has a solution, it will have more than 1)

    3. My attempt at a proof:
    Well, I'm stuck as to the interpretation, and where to even begin for that matter. If you have any hints/tips that could get me started, that would be great. I don't want an answer, just a little scaffolding to get me there.

    Any input is greatly appreciated. It means a lot when people help :blushing:
     
  2. jcsd
  3. Sep 21, 2010 #2
    b is a zero divisor seems to be important. Try using that by left multiplying bx by non zero y where yb = 0.
     
  4. Sep 23, 2010 #3

    silvermane

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    Gold Member

    Yeah this is very helpful! Thank you!
     
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