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REA book review question

Posted: Thu Oct 04, 2012 11:07 pm
by 26186514
on Page 90, sample test 2, problem 62:
Let R be a ring and let x<>0 be a fixed element in R. Which of the followin is a subring of R?
In the choices, there is one {nx|n is an integer}.
I think this is a subring, since rings do not have to be closed under multiplication. However, the answer gives no.
Any idea?

Re: REA book review question

Posted: Fri Oct 05, 2012 3:33 am
by vonLipwig
Some people require that a subring contain the multiplicative identity.

Re: REA book review question

Posted: Fri Oct 05, 2012 6:26 am
by PNT
Rings do have to be closed under multiplication

Re: REA book review question

Posted: Fri Oct 05, 2012 1:32 pm
by 26186514
oh yes... thanks for the reply. I got it now.