Spring 2024 Algebra (under construction)
上課時間: 週三67，週五678.
上課地點: 天數101
Office hour: 週三3:30--5:30 at 天數412
The purpose of this course is to introduce basic tools in
non-commutative rings and commutative algebra.
The goal is to equip students with standard knowledge to study
advanced topics
in representation theory, number theory and algebraic geometry.
References:
Noncommutative algebra, B. Farb and K. Dennis
(GTM144)
Algebra Chapter 8, Modules et anneaux
semi-simples, N. Bourbaki.
Introduction to
commutative algebra,
Atiyah-Macdonald.
Commutative algebra with a
view toward algebraic geometry, D.
Eisenbud (GTM150)
Syllabus:
Theory of semi-simple rings and
applications
Week 1:
Semisimple modules.
Week 2: The
Weddburn-Artin Theorem
Week
3: Density theorem, simple rings and the
Jacobson radical
Week 4: Jacobson's theorem. Tensor products of modules.
Week 5: Central simple algebras and the Skolem-Noether
Theorem.
Week 6-7: Brauer groups and K_2
groups of fields.
Week 8: Midterm.
Introduction to commutative algebras:
theory of affine schemes
Week
9 : The language of affine schemes.
Week 10: Algebras of finite type over a field
and Hilbert's Nullstellensatz.
Week 11: Etale morphisms and de Rham
cohomology of affine schemes.
Week
12: Basic homological
algebras: injective
resolutions, derived
functors and spectral
sequences.
Week 13:
Noetherian rings and Hilbert's basis theorem.
Week
14: Heights of primes
and principal ideal
theorem.
Week 15: Zariski's main theorem and
Chevalley's theorem
Week 16: Final exam
習題課時間: 每週五第八節
助教: 李俊緯
(d09221001AT ntu.edu.tw)
作業: 繳交每週
發佈於NTU
Cool的作業。
評量方式:
作業 (30%) 週五第八節結束前繳交，請利用NTU COOL上傳作業， 逾期不收。
期中考(35%) April 10,
12:30--15:10 (Week 1-6)
期末考(35%) June 7, 13:30-15:10