# Ring, Integral Domain

• May 15th 2011, 01:06 PM
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?
• May 15th 2011, 01:11 PM
tonio
Quote:

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
• May 15th 2011, 01:12 PM
TheEmptySet
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