Fundamental concepts in commutative algebra,
- November 7. We got new
rooms for lectures. I updated the general info in accordance.
- October 31. Due to your
request, the deadline for submitting homework will be on Thursdays
midnight, starting with HW1 (which should now be submitted on November 2).
- October 22. The lecture on
October 24 will be given by Uri Brezner.
· Michael Temkin
· E-mail: temkinmath.huji.ac.il
· Office: Ros 78A (tel. 02-6584575)
· Office Hours: by appointment
· Lectures: Mondays 10-11:45 at Ros 70,
Tuesdays 16-17:45 at Mathematics 110.
· Uri Brezner
· E-mail: uri.breznermail.huji.ac.il
· Office: Ros 26 (tel. 02-6584846)
· Office Hours: by appointment
· Recitations: Tuesdays 12-13:45 at Sprinzak
· The commutative algebra part will be due to
"Introduction to Commutative Algebra" by Atiyah and Macdonald.
· The final grade will be obtained as follows:
50% of the exam grade plus 50% of the homework grade. The grade for homework
will be computed by averaging 10 best weekly homework grades.
The exam will be only
on the commutative algebra part of the course, and an exam syllabus will be
posted in the end of the course.
· The exercises are assigned on
Tuesdays on this webpage, and should be submitted to Uri's mailbox until the
end of the next Thursday (any time before 24:00 is ok). Late (or non-submitted)
homework will not be graded. Homework may include a non-mandatory part marked
by *, which is not for submission but can be helpful for deeper understanding
of the material. You are welcome to discuss it with me or Uri.
More difficult problems are marked
- October 24. The first homework is here. Due date
is October 31. (Changed to November 2.)
- October 31. The second homework is here. Due date
is November 9.
- November 7. The third homework is here. Due date
is November 16.
- November 14. The fourth homework is here. Due date
is November 23.
- November 21. The fifth homework is here. Due date
is November 30.
- October 23. Some basic definitions from chapter 1, including
commutative rings with units, their homomorphism, R-algebras, polynomial
rings, maximal/prime/principal ideals, quotient rings, nilpotent elements
and zero divisors.
- October 24. End of chapter
1 and some exercises after it: extension and contraction of ideals with
respect to a homomorphism, Chinese remainder theorem, some properties of
- October 30. Beginning of
chapter 3: localizations of rings, its universal property, and behavior of
ideals under localization.
- October 31. Categories,
limits and colimits (including products and coproducts, fibred products,
equalizers and coequalizers), complete and cocomplete categories. Criteria
of completeness and cocompleteness. Here
are my written notes about categories. (Two precautions: (1) I'll polish
it and maybe add some details, (2) The order of exposition is different. I
introduce representable functors first and deduce the criteria from Yoneda
lemma. We will study (or at least formulate) this next week.)
- November 6. Adjoint
functors, continuous and cocontinuous functors.
- November 7. Started
R-modules (beginning of chapter 2). Definitions, submodules, quotients,
limits and colimits, kernels and cokernels.
- November 13. Different
versions of Nakayam lemma, additive invariants and K_0 of subcategories of
R-Mod, exact sequences, the snake lemma.
- Novemer 14. Bilinear maps,
tensor products, adjunction between tensor products and Hom's, exactness
properties of tensor products and Hom's, further properties of tensor
- November 20. Extension of
scalars, localization of modules.
- November 21. Classification
of adjoint pairs of functors between categories of modules, tensor products
of algebras and basic examples, including quotients, localizations,
products of field extensions. Definition of flat modules.