Answer to Question #351026 in Abstract Algebra for Fed

Question #351026

3.7 If D is an integral domain and if na = 0 for some a #= 0 in

D and some integer n #= 0, prove that D is of finite characteristic.


1
Expert's answer
2022-06-22T09:43:29-0400

Let "b\\in D". Consider "nab". Since "(na)=0" we have "nab=0". On the other hand, "nab=nba" as the integral domain is a commutative ring. So "0=nab=nba". But "a\\ne 0" implies "nb=0" for all "b\\in D".


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