WSA21000 Algebra A

Hiroshima University Syllabus

Japanese

Academic Year 2022Year School/Graduate School Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program

Lecture Code WSA21000 Subject Classification Specialized Education

Subject Name 代数数理基礎講義Ａ

Subject Name
（Katakana）ダイスウスウリキソコウギエー

Subject Name in
English Algebra A

Instructor MATSUMOTO MAKOTO

Instructor
(Katakana) マツモト　マコト

Campus Higashi-Hiroshima Semester/Term 1st-Year, First Semester, 1Term

Days, Periods, and Classrooms (1T) Weds5-6,Fri3-4

Lesson Style Lecture Lesson Style
(More Details) 　

Mainly on black board.

Credits 2.0 Class Hours/Week 　 Language of Instruction B : Japanese／English

Course Level 5 : Graduate Basic

Course Area（Area） 25 : Science and Technology

Course Area（Discipline） 01 : Mathematics/Statistics

Eligible Students

Keywords

Special Subject for Teacher Education 　 Special Subject 　

Class Status
within Educational
Program
Criterion referenced
Evaluation

Class Objectives
/Class Outline For a ring R, we define the notion of R-action on an addive group M. Such object M is called an R-module. If R is a field, then this notion coincides with the notion of K-vector space. In this lecture, we investigate the properties of R-modules, which is a basis of many areas in mathematics, in particular homological algebra and algebraic geometry.

Class Schedule lesson1 Recall rings and additive groups
lesson2 Direct sum, direct product, free R-modules
lesson3 Exact sequence and commutative diagram
lesson4 Elementary divisor I
lesson5 Elementary divisor II
lesson6 Structure of finitely generated module over R
lesson7 Jordan normal form
lesson8 Tensor product
lesson9 Flat module
lesson10 Projective module
lesson11 Injective module
lesson12 Noetherian property
lesson13 Finitely generated commutative ring over Noetherian ring is again Noetherian
lesson14 Introduction to semisimple ring
lesson15 Wedderburn's theorem

Report will be required

When necessary, the lecture is given in English.

Text/Reference
Books,etc. Will be explained at the first lecture, but any books on ring and modules will work.

PC or AV used in
Class,etc. 　

(More Details) Black board and printed lecture-note (pdf will be available from the URL shown below).

Learning techniques to be incorporated 　

Suggestions on
Preparation and
Review Needs intensive self-learning, in particular concrete examples computed by one's own hand.

Requirements

Grading Method Report (around 80%), and attitude to the lecture

Practical Experience

Summary of Practical Experience and Class Contents based on it

Message

Other Lecture note (pdf, Japanese) will be available from
http://www.math.sci.hiroshima-u.ac.jp/~m-mat/TEACH/teach.html

Please fill in the class improvement questionnaire which is carried out on all classes.
Instructors will reflect on your feedback and utilize the information for improving their teaching.

Academic Year	2022Year	School/Graduate School	Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program
Lecture Code	WSA21000	Subject Classification	Specialized Education
Subject Name	代数数理基礎講義Ａ
Subject Name （Katakana）	ダイスウスウリキソコウギエー
Subject Name in English	Algebra A
Instructor	MATSUMOTO MAKOTO
Instructor (Katakana)	マツモト　マコト
Campus	Higashi-Hiroshima	Semester/Term	1st-Year, First Semester, 1Term
Days, Periods, and Classrooms	(1T) Weds5-6,Fri3-4
Lesson Style	Lecture	Lesson Style (More Details)
Mainly on black board.
Credits	2.0	Class Hours/Week		Language of Instruction	B : Japanese／English
Course Level	5 : Graduate Basic
Course Area（Area）	25 : Science and Technology
Course Area（Discipline）	01 : Mathematics/Statistics
Eligible Students
Keywords
Special Subject for Teacher Education		Special Subject
Class Status within Educational Program
Criterion referenced Evaluation
Class Objectives /Class Outline	For a ring R, we define the notion of R-action on an addive group M. Such object M is called an R-module. If R is a field, then this notion coincides with the notion of K-vector space. In this lecture, we investigate the properties of R-modules, which is a basis of many areas in mathematics, in particular homological algebra and algebraic geometry.
Class Schedule	lesson1 Recall rings and additive groups lesson2 Direct sum, direct product, free R-modules lesson3 Exact sequence and commutative diagram lesson4 Elementary divisor I lesson5 Elementary divisor II lesson6 Structure of finitely generated module over R lesson7 Jordan normal form lesson8 Tensor product lesson9 Flat module lesson10 Projective module lesson11 Injective module lesson12 Noetherian property lesson13 Finitely generated commutative ring over Noetherian ring is again Noetherian lesson14 Introduction to semisimple ring lesson15 Wedderburn's theorem Report will be required When necessary, the lecture is given in English.
Text/Reference Books,etc.	Will be explained at the first lecture, but any books on ring and modules will work.
PC or AV used in Class,etc.
(More Details)	Black board and printed lecture-note (pdf will be available from the URL shown below).
Learning techniques to be incorporated
Suggestions on Preparation and Review	Needs intensive self-learning, in particular concrete examples computed by one's own hand.
Requirements
Grading Method	Report (around 80%), and attitude to the lecture
Practical Experience
Summary of Practical Experience and Class Contents based on it
Message
Other	Lecture note (pdf, Japanese) will be available from http://www.math.sci.hiroshima-u.ac.jp/~m-mat/TEACH/teach.html
Please fill in the class improvement questionnaire which is carried out on all classes. Instructors will reflect on your feedback and utilize the information for improving their teaching.

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