2024 Students Enrolled in or before 2015 School of Science Mathematics
Exercises in Algebra B I
- Academic unit or major
- Mathematics
- Instructor(s)
- Masatoshi Suzuki
- Class Format
- Exercise (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Thu
- Class
- -
- Course Code
- ZUA.A302
- Number of credits
- 020
- Course offered
- 2024
- Offered quarter
- 1-2Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
This course is an exercise session for the lecture course "Algebra I (ZUA.A301)". The materials for exercise are chosen from that course.
Course description and aims
By the end of this course, students will be able to:
1) Understand the notions of (commutative) rings and modules over rings.
2) Understand tensor products and make use of them correctly.
3) Understand localization and make use of them correctly.
4) Understand the notion of Noethrian and Artinian rings, and make use of fundamental operations for them correctly.
5) Understand the notion of local rings, and make use of fundamental operations for them correctly.
6) Understand homological algebra, and make use of fundamental operations for them correctly.
Keywords
rings, ideal, residue rings, modules, tensor products, localization, Noetherian rings, Artinian rings, local rings, homological algebra
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
Students are given exercise problems related to what is taught in the course "Algebra I".
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Discussion session on the following materials: Rings and ideals | Details will be provided during each class session. |
| Class 2 | Discussion session on the following materials: Modules over a ring, submodules, homomorphisms | Details will be provided during each class session. |
| Class 3 | Discussion session on the following materials: Free modules, exact sequences | Details will be provided during each class session. |
| Class 4 | Discussion session on the following materials: Modules over a PID | Details will be provided during each class session. |
| Class 5 | Discussion session on the following materials: Localization | Details will be provided during each class session. |
| Class 6 | Discussion session on the following materials: Noetherian rings and Artinian rings | Details will be provided during each class session. |
| Class 7 | Discussion session on the following materials: Hilbert's basis theorem | Details will be provided during each class session. |
| Class 8 | Discussion session on the following materials: Local rings | Details will be provided during each class session. |
| Class 9 | Discussion session on the following materials: Semi-simple rings | Details will be provided during each class session. |
| Class 10 | Discussion session on the following materials: Tensor product, right exactness of tensor product | Details will be provided during each class session. |
| Class 11 | Discussion session on the following materials: Flat modules, Projective modules, Injective moduls | Details will be provided during each class session. |
| Class 12 | Discussion session on the following materials: Five lemma, Snake lemma | Details will be provided during each class session. |
| Class 13 | Discussion session on the following materials: Advanced topics | Details will be provided during each class session. |
| Class 14 | Discussion session on the following materials: Advanced topics | Details will be provided during each class session. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
TBA
Reference books, course materials, etc.
This will be announced during the lecture.
Evaluation methods and criteria
This will be announced during the lecture.
Related courses
- MTH.A301 ： Algebra I
- MTH.A302 ： Algebra II
- MTH.A201 ： Introduction to Algebra I
- MTH.A202 ： Introduction to Algebra II
- ZUA.A301 ： Algebra I
Prerequisites
Students must have successfully completed [Linear Algebra I/Recitation], Linear Algebra II, Linear Algebra Recitation II, Advanced Linear Algebra I, II and Introduction to Algebra I, II, III, IV; or, they must have equivalent knowledge.
Students are strongly recommended to take ZUA.A301: Algebra I (if not passed yet) at the same time.
Other
None in particular.