Another source that might come in handy is
I'll probably ask you to read some of the sections in the textbook before most lectures, so we're in sync. I'll post the reading assignments here. Unless specified otherwise the sections are those in Dummit-Foote.
The date is that of the lecture, so please do the reading before that.
| Due date | Assignment | Remarks | |
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| 1 | Th Sep 11 | 7.1, 7.2, 7.3, 7.4, 7.5 Appendix II (category theory) |
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| 2 | Th Sep 18 | 10.2, 10.3, 10.4 |
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| 3 | Th Sep 25 | 10.5 |
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| 4 | Th Oct 02 | 13.1, 13.2 |
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| 5 | Th Oct 16 | 13.4, 13.5 |
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| 6 | Th Oct 23 | 13.6, 14.1 |
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| 7 | Th Oct 30 | 14.2 |
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| 8 | Th Nov 06 | 14.3, 14.4 |
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| 9 | Th Nov 13 | 14.5, 14.6 |
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No classes the whole week of Nov 24 |
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On occasion I'll post extra notes, comments, etc. in this space.
Regarding injective abelian groups: the characterization result equating injectivity and divisibility is proven here, and you can find the classification as Theorem 4 in Kaplansky's Infinite Abelian Groups.
The classification of semisimple rings is carried out in Theorem 3.5 of [Lam]. More generally, Sections 2 and 3 of that book are all about semisimplicity, so you will see a number of alternative characterizations there.
There are a great many sources that will cover as much as what I said on adjoint functors and (co)product preservation and more. [Borceux1, Proposition 3.2.2] is the full common generalization of the claim that right adjoints preserve products and are left exact, but you will also have to read up on limits and colimits to do that statement justice. A textbook account is in [Borceux1, 2.6].
Alternative source (perhaps better, because freely available: just click!): [AHS, Section 11] for background on (co)limits and [AHS, Proposition 18.9] for the limit-preservation claim.
We exchange homework via UBLearns: I post the assignments there through the 'Assignments' facility provided by the system and you'll similarly be able to upload files.
No late homework for any reason, but we are dropping the two lowest scores.
| Due date | Assignment | Remarks | |
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| 1 | Th Sep 11 |
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| 2 | Th Sep 18 |
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| 3 | Th Sep 25 |
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| 4 | Th Oct 02 |
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| exam 1 | Th Oct 09 |
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No homework this week |
| 5 | Th Oct 16 |
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| 6 | Th Oct 23 |
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| 7 | Th Oct 30 |
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| 8 | Th Nov 06 |
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| 9 | Th Nov 13 |
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| exam 2 | Mo Dec 08 |
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We're done! |
The grader will assign each homework a grade out of 10 with only a few problems being graded (3 or 4 or so). There will also be points awarded for the overall completeness of the assignment. I won't be telling you in advance which problems are being graded though..
Do collaborate on the homework if you like, but write up your own solutions. I also strongly advise you to have a look at the UB Academic Integrity Policy, as it very much applies to this class.
And by all means drop by at office hours if you need a hand.
We're having two take-home exams. The dates are as follows
Those are the due dates. I will post the problem lists a few days before, so you will have plenty of time to work on them.
We'll drop the two lowest homework scores.
If you have any questions, don't hesitate to email me.
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