FALL 2014

Math 461 --- RINGS AND MODULES

Announcement : EXAM 1 is on October 24, Friday 17:30 (covers Chp 1)

Prerequisite: Math 367 or consent of instructor. Credits: (3-0) 3.

Instructor: Semra Öztürk Kaptanoğlu, M 138, Schedule and office hours are at the address http:/www.metu.edu.tr/~sozkap/AA.pdf.

Web page of the course is at http://www.math.metu.edu.tr/~sozkap/461-2014 ,

Cataloque Contents: Rings, ideals, isomorphism theorems, group rings, localization, factor rings. Modules, submodules, direct products, factor modules. Homomorphisms, classical isomorphism theorems. The endomorphism ring of a module. Free modules, free groups. Tensor product of modules. Finitely generated modules over a principal ideal domain.  

Grading will be based on the exams. There will be only one make -up exam for any of the exams missed. It will be after the final exam and you should have your instructors permission to be able to take it.

Description of the course

As the title suggests this course consists of two parts, rings and modules. Rings will be expanded version of what you have seen in Math 367, and also Math 116 with the addition of localization. Since my interest is in modules over group algebras I will bring in examples from those. We will spend two thirds of the semster for rings (about 8-9 weeks).

Modules will be new to you. They are generalizations of vector spaces. In spirit module theory is a generalization of linear algebra.

(about 6 weeks).

I. Rings, main titles are: Rings, ideals, homorphism of rings, group algebras .  II. Modules, main titles are: Modules, free modules, quotient modules, modules over a PID, modules over group algebras (if time permits).

We will use the following book.

Textbook: Introduction to Rings and Modules, Second Revised Edition, by C. Musili, Narosa Publishing House, 1994

I will follow the book section by section. It has 6 chapters, we must cover the first five chapters about 150 pages in total.

Chapters 1—4 are on rings, only Chapter 5 is on modules so I will expand it a little bit.

This course is to provide the background for students who are willing to learn more about rings which are the common mathematical structures occuring everywhere J! It is good for everyone J but especially for students who are

planning to study any algebra related topics such as algebraic topology, algebraic geometry.

MATEMATiK NASIL OKUNUR YAZILIR v.s.(İngilizce kaynaklar)