Talk:07-401/Homework Assignment 1

Email of Jan 14

Hello Professor,

Regarding the first homework, in question 2 and 13 (p.241), do we need to
justify our answers?  In #2, this would mean systematically checking our
candidate for unity with the other ring elements.  In #13, do we just list
possible subrings?  Lastly, in question 24 (p.255), do we just verify the
axioms because some of the instances seem "almost" trivial.  Please reply at
your convenience.  Thanks.

Sincerely,

***

Answer by Dror. You always need to justify your answers. Though in #2, for example, you don't need to justify what is not your answer. Thus you do need to check that your proposed unity is indeed a unity, but you don't need to explain why all other elements are not unities (though that follows automatically from the uniqueness of the unity).

In #13, an ok solution is just the list of subrings. An excellent solution would also contain a verification that each of the listed subrings is indeed a subring and a that no other subrings exist.

For question 24 (p.255), it is ok to dismiss some of the most trivial verifications as "trivial", but you do need to verify explicitly the few that are harder.