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

EnglishAlgebra 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

ProgramCriterion referenced

EvaluationClass Objectives

/Class OutlineFor 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

ReviewNeeds 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.htmlPlease 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.