Hiroshima University Syllabus

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Academic Year School/Graduate School Lecture Code 2022Year Graduate School of Advanced Science and Engineering (Master's Course) Division of Advanced Science and Engineering Mathematics Program WSA21000 Specialized Education 代数数理基礎講義Ａ ダイスウスウリキソコウギエー Algebra A MATSUMOTO MAKOTO マツモト　マコト Higashi-Hiroshima 1st-Year,  First Semester,  1Term (1T) Weds5-6,Fri3-4 Lecture Mainly on black board. 2.0 B : Japanese／English 5 : Graduate Basic 25 : Science and Technology 01 : Mathematics/Statistics 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. lesson1 Recall rings and additive groupslesson2 Direct sum, direct product, free R-moduleslesson3 Exact sequence and commutative diagramlesson4 Elementary divisor Ilesson5 Elementary divisor IIlesson6 Structure of finitely generated module over Rlesson7 Jordan normal formlesson8 Tensor productlesson9 Flat modulelesson10 Projective modulelesson11 Injective modulelesson12 Noetherian propertylesson13 Finitely generated commutative ring over Noetherian ring is again Noetherianlesson14 Introduction to semisimple ringlesson15 Wedderburn's theoremReport will be requiredWhen necessary, the lecture is given in English. Will be explained at the first lecture, but any books on ring and modules will work. Black board and printed lecture-note (pdf will be available from the URL shown below). Needs intensive self-learning, in particular concrete examples computed by one's own hand. Report (around 80%), and attitude to the lecture 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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