Hiroshima University Syllabus

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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
Subject Name in
Algebra A
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
Special Subject for Teacher Education   Special Subject  
Class Status
within Educational
Criterion referenced
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. 
Will be explained at the first lecture, but any books on ring and modules will work. 
PC or AV used in
(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
Needs intensive self-learning, in particular concrete examples computed by one's own hand. 
Grading Method Report (around 80%), and attitude to the lecture 
Practical Experience  
Summary of Practical Experience and Class Contents based on it  
Other Lecture note (pdf, Japanese) will be available from
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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