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Sep 22 at 20:02 comment added Z Wu For the first statement, we need to assume $1\neq 0$ in $A$. Otherwise (i) and (ii) are trivially true and (iii) is false because an integral domain is nonzero by definition.
Mar 9, 2016 at 8:48 comment added ACL See Martin's answer there (a reference to Lam's book on modules and rings): math.stackexchange.com/questions/400776/…
Jan 30, 2011 at 15:39 comment added Joy-Joy @Konstantin Ardakov: You are right. Thanks a lot for the detailed explaination!
Dec 29, 2010 at 0:08 history answered Joy-Joy CC BY-SA 2.5