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Math Help - Ring, Integral Domain

  1. #1
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    Ring, Integral Domain

    If R is a ring and a\neq 0\in R and ab=ca, then b=c. How can I show that R is an integral domain?
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    Quote Originally Posted by road View Post
    If R is a ring and a\neq 0\in R and ab=ca, then b=c. How can I show that R is an integral domain?


    Suppose a\neq 0\,\,and\,\,a\cdot b=0=a\cdot 0 . and now use the given data.

    Tonio
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  3. #3
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    Quote Originally Posted by road View Post
    If R is a ring and a\neq 0\in R and ab=ca, then b=c. How can I show that R is an integral domain?
    As written the above statement is not true unless R is a commutative ring.
    Last edited by TheEmptySet; May 15th 2011 at 03:05 PM. Reason: spelling
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