Answer to Question #350990 in Abstract Algebra for deq

Question #350990

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
2022-06-20T13:09:17-0400

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\\ne0" implies "nb=0" for all "b\\in D".


Need a fast expert's response?

Submit order

and get a quick answer at the best price

for any assignment or question with DETAILED EXPLANATIONS!

Comments

No comments. Be the first!

Leave a comment

LATEST TUTORIALS
New on Blog
APPROVED BY CLIENTS