# MA3G6 Commutative Algebra

## MA3G6 Commutative Algebra Sheet 1 solutions 6 posts 0 followers RSS feed

You need to be logged in to post in this topic.
1. Solutions to sheet 1 are now online. Please ask if anything is not clear. After your assignments have been marked I’ll post general feedback online too.

2. Re: Sheet 1 solutions
> Solutions to sheet 1 are now online. Please ask if > anything is not clear. After your assignments have > been marked I’ll post general feedback online too. Feedback on your solutions to Sheet 1 are now online, written by Michael after marking. It might be a good idea to look at these between now and today’s handing in deadline for Sheet 2!

3. Re: Sheet 1 solutions
> Solutions to sheet 1 are now online. Please ask if > anything is not clear. After your assignments have > been marked I’ll post general feedback online too. Michael writes: > a couple of students came up with a different (and in my opinion cleaner) > way of answering question 2 i). > > > First assume R is an integral domain. Then if f is a unit with fg = 1 then > f and g must be constant (since deg(fg) = deg(f) + deg(g) over an integral > domain). Now let R be general, and P any prime ideal in R. By the above, if > fg = 1 this also holds reducing coefficients mod P, so that f is a constant > mod P. In particular all higher coefficients are in P. Since P was > arbitrary, they are in all the prime ideals, hence nilpotent. > > That is fantastic, and much better than my solution (which follows the hint in Atiyah-Macdonald).

4. Re: Sheet 1 solutions
Have the assignments for sheet 1 been distributed back to the students? I just checked my pigeon hole today and didn’t find my assignment.

5. Re: Sheet 1 solutions
Hi Nyeok, I was just about to email you as I spectacularly failed to locate your pigeonhole, I think because I was looking under “Nyeok” rather than “Lee”. I’ll get it to you on Monday. Sorry for the inconvenience. Everyone else should now have their scripts back though. If you don’t and you submitted work, then that is serious because either I never got it, or I’ve lost it, so you should let me know. All the best, Michael

6. Re: Sheet 1 solutions
Hi Michael, Thank you for the prompt reply. No problem at all and I should’ve written my name in the standard format. Sorry for the inconvenience. Kind regards, Kit