ALGEBRA II

Teaching Staff in AY1997 : Hiroshi SUZUKI
- Office : NS-S309, Tel.:3292, E-mail:hsuzuki@icu.ac.jp
Term and Schedule : Autumn Term, Mon + Thurs 4
Class Room : NS-S312
Class Schedule
Refernces
List of Exercises
- Ex.1, Ex.2, Ex.3, Ex.4, Ex.5,
  Ex.6, Ex.7, Ex.8, Ex.9
AY1997 Midterm Test
Solution: Prob. 1, Prob. 2, Prob. 3, Prob. 4
AY1996 Midterm Test
AY1996 Final Test
AY1995 Final Test
Classes in AY1997
Index

Month/Day	Title	Subjects
September 8	Ring, Field, Integral Domain	Definitions and basic properties
11	Ideals and Factor Rings	Principal Ideal Domain, Eucideal Domain
18	Recitation
22	Recitation
25	Isomorphism Theorem	Homomorphism, Minimal Polynomial
29	Prime Ideals and Maximal Ideals	The condition for factor ring to be integral domain or field
October 2	Recitaion
6	Recitation
9	Direct Sum of Rings	Coprime ideals, Chinese Remainder Theorem
13	Quotient Rings	Localization, Local Ring
16	Recitation
20	Recitation
23	Unique Factorization Domain 1	PID is UFD
27	Recitation ?	Midterm ?
30	Unique Factorization Domain 2	Polynomial ring over UFD is UFD
November 6	Recitation
10	Recitation
13	R-modules	R-modules and R-algebra,maximal and minimal conditions
17	Recitation

Take-Home Midterm is scheduled in mid May.
Final will be given during the final week.
Recitation problems are not assigned. Please solve them and present them on the board voluntarily.

Hiroshi Nagao, "Daisugaku", Asakura Publisher (in Japanese)

Very well written and widely used but a bit difficult for individual study. This text book will be used in Algebra II and III.

(References for Algebra including groups, rings, fields and modules

Serge Lang "Undergraduate Algebra" second edition, Springer-Verlag
Widely used text book. Lang writes a lot of popular text books.
Serge Lang "Algebra" third edition, Addison-Wesley Graduate student's level text book. The material is widely covered but it is possible to read. I, Suzuki, read this as students seminar with friends from sophomore to senior when I was a student.
van der Waerden "Modern Algebra", Springer
Classical text book.
M. F. Atiyah and I. G. Macdonald　"Introduction to Commutative Algebra", Addison-Wesley
Ring Theory can be classified into "Commutative Ring Theory" and "Noncommutative Ring Theory". "Commutaive Ring Theory' gives the basis of Number Theory and Algebraic Geometry and the typical examples are the ring of rational integers Z and the polynomial ring over a field K[x₁,...x_n]. This book gives an introduction to "Commutative Ring Theory". As for the "Noncommutative Ring Theory" is related to, for example, representation theory using the theory of semisimple rings. The typical examples are the ring of matrices. Please refer to the next book.
C. W. Curtis and I. Reiner "Representation theory of finite groups and associative algebras", Wiley－Interscience Publication