Talk:07-401/Homework Assignment 1

General Note

In principle I much prefer that questions about HW (or any other thing) be asked and answered on the "Talk" pages for that HW assignment (or other relevant page). That way other students may read the questions and answers, and I (Dror) don't need to answer the same questions again and again.

I've copied here a couple of email questions that I got. In the future, please post your questions directly on the "Talk" pages.

--Drorbn 09:23, 17 January 2007 (EST)

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.

Email of Jan 16

Dear Prof,

I have some questions about HW one:
chapter 12 question 13: after describe the form of all the subrings of Z,
do we need to prove that any subrings of Z is in the form we found?

Answer by Dror. See above.

Is that true that R is a ring if only if it's closed under the addition
and multiplication ( or use the subring test to say that R is a ring if
only of it is non-empty and closed under subtraction and multiplication?)

Answer by Dror. Addition and multiplication would not be enough to determine a subring, you also need to know about negatives. Replacing addition by subtraction covers that too.

for chapter 13 question 13: Can I assume that the unity is 1?( otherwise,
i can't use the hint)

Answer by Dror. Yes.

If you don't have time to reply, can I make an appoitment with you for
this Wednesday before lecture?

Best,

***