ABSTRACT

LECTURES ON COMMUTATIVE ALGEBRA

SHIRO GOTO

Lecturer: Prof. Shiro Goto, Meiji University, Tokyo, Japan

Part I.January 9 (Monday), 8:00-11:00 (including a break)

This is a lecture for the students of undergraduate courses. I plan to talk about what is commutative algebra, including:

(1) History and the personality of Emmy Noether

(2) The ring Z of integers as a model of Noetherian rings

(3) Denition of Noetherian rings

(4) Examples from numerical semigroups

(5) Hilbert’s basis theorem

(6) Primary decomposition of ideals and associated primes

(7) Modern development (a brief history) of commutative algebra

Part II.January 10 (Tuesday) 8:00-11:00 (including a break)

This is a lecture for the student of graduate courses. I plan to talk about a few results based on the lecture note [G], including:

(1) Hierarchy of Noetherian local ring and what is homological methods in commutative algebra

(2) Associated primes of modules

(3) Serre’s theorems on regular local rings

(4) Examples

[G] SHIRO GOTO, Homological Methods in Commutative Algebra, VIASM, 2016.

1. What is CA.pdf: http://www.mediafire.com/file/nd9spduamk4bxe7/What_is_CA.pdf

2. School Note.pdf: http://www.mediafire.com/file/pa6hqg0gemiwcfx/School_Note.pdf