**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 4: Jacobson's theorem. Tensor products of modules.

Week 5: Central simple algebras and the Skolem-Noether Theorem.

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 15: ???

Week 16: Final exam

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)**