Coordinator: Zhou Yang (周杨)
Email: wooonderfulworld AT gmail DOT com
Mobile: 150 6815 1550 (514379)
Textbook: Algebra, by Michael Artin
2011.09.18.
10.1-Definition of a ring
10.2-Formal construction of integers and polynomials
speaker: Zhou Yang(周杨)
2011.09.25.
10.2-Homomorphisms and ideals
10.4-Quotient rings and relations in a ring
speaker: Guo Zhengyang(郭正扬), Hu Kanghao（胡康豪）
2011.10.02.
10.5-Adjunction of elements
10.6-Integral domains and fraction fields
speaker: Qian Wei(钱炜), Wang Jun(王俊)
2011.10.16.
10.7-Maximal ideals
Review of the exercises in Chapter 10
speaker: Lv Renjie(吕人杰)
2011.10.23.
11.1-Factorization of integers and polynomials
11.2-UFD, PID, and ED
speaker: Lv Renjie(吕人杰), Qian Wei(钱炜)
2011.10.30.
11.3-Gauss’ Lemma
11.4-Explicit factorization of polynomials
11.5-Primes in the ring of Gauss integers
speaker: Wang Jun(王俊), Lv Renjie(吕人杰)
2011.11.13.
11.6 Algebraic integers
11.7-Factorization in imaginary quadratic fields
speaker: Hu Kanghao（胡康豪）
2011.11.20.
11.8-Ideal factorization
11.9-Prime ideals of R and prime integers
speaker: Zhang Hanyu(张寒煜)
2011.11.27.
10.10-Ideal classes in imaginary quadratic fields
10.11-Real quadratic fields
speaker: Lv Renjie(吕人杰), Guo Zhengyang(郭正扬)
2011.12.04.
10.12-Some Diophantine equations
Review of the exercises in Chapter 11
speaker: Zhang Hanyu(张寒煜)
2011.12.11.
12.1-The definition of a module
12.2-Matrices, free modules, and bases
12.3-The principle of permanence of identities
speaker: Hu Kanghao（胡康豪）
2011.12.18.
12.4-Diagonalization of integer matrices
12.5-Generators and relations for modules
speaker: Lv Renjie(吕人杰)
2011.12.25.
12.6-The structure theorem for abelian groups
speaker: Vacant
2012.01.01.
12.7-Applications to linear operators
12.8-Free modules over polynomial rings
Review of the exercises in Chapter 12
speaker: Vacant
This is a continuation of the same seminar in the summer. We’ll cover Chapters 10 and 11 on rings and Chapter 12 on modules. The chapters on fields and Galois Theory will be studied in a continuing seminar next semester, which will synchronize with the course in abstract algebra.