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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Originally Posted by road 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 $\displaystyle a\neq 0\,\,and\,\,a\cdot b=0=a\cdot 0$ . and now use the given data. Tonio
Originally Posted by road 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 02:05 PM. Reason: spelling
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