HOME PAGE OF MATH 5020:

Introduction to
Commutative Algebra

Fall 2012

INSTRUCTOR:

Sarah Glaz

glaz@math.uconn.edux (click on link and remove end x)

Office: MSB 202

Phone: (860) 486 9153

CLASS:

T, Th 12:30 - 1:45, MSB 117

BOOKS:

Main Textbook: Introduction
to
Commutative Algebra, by M.F. Atiyah & I.G. MacDonald,
Academic Press, Inc.

(May be ordered new or used from
amazon.com, or other reliable online used book sites like
alibris.com, abebooks.com, or strandbooks.com)

Other Texts (you need not purchase):

Commutative
Algebra, by Bourbaki

Commutative
Coherent
Rings, by Sarah Glaz

Multiplicative Ideal Theory, by Robert Gilmer

Commutative Rings with
Zero-Divisors, by James Huckaba

Commutative Rings, by Irving
Kaplansky

Commutative Ring Theory,
by Hideyuki Matsumura

COURSE OUTLINE:

Commutative Algebra,
the study of commutative rings and their modules, emerged as a
definite area of mathematics at the beginning of the twentieth
century. Its origins lie in the works of eminent
mathematicians such as Kronecker, Dedekind, Hilbert and Emy
Noether who sought to develop a solid foundation for Number
Theory. Later, the field was enriched by its relation to
modern Algebraic Geometry, Topology, Homological Algebra, and
Combinatorics. Today Commutative Algebra is a deep and
beautiful area of study in its own right, which both draws on,
and is applicable to, all the disciplines that contributed to
its development. In this course we will study the fundamental
notions and methods of research of commutative algebra. Topics
will include: basic module and ideal notions and constructions
(such as prime ideals, zero-divisors, localizations, primary
decomposition, integral dependence, completions, and dimension
theory), special types of rings (such as valuation rings,
Krull domains, Noetherian rings, Artinian rings, and coherent
rings), and homological algebra aspects of commutative algebra
(such as projectivity, flatness, grade, and factorization
properties). Other topics may be introduced as time allows. We
anticipate covering most of Chapters 1 - 11 from the
main textbook, supplemented from the other texts mentioned
above.

GRADING:

Grading would be based on a homework grade (50%), and a
semester project grade (50%). There will be 3 - 5 homework
assignments, each comprising of a number of exercises.
Students are encouraged to discuss the homework assignments
with each other, but need to formulate, write, and hand in
their own individual solutions. The semester project will be
on a topic chosen by the instructor in collaboration with each
student. Each students will hand in a typed report (5 - 10
pages) and give a class presentation on his/her project.
Topics will be assigned a few weeks into the semester. Reports
and presentations will begin in November.

SPECIAL DAYS:

First Day of Classes: Monday, August 27

Labor Day (no classes): Monday, September 3

No class: Tuesday, September 18

Thanksgiving Break: Sunday, November 18 - Sunday, November 25

Last Day of Classes: Friday, December 7

HOMEWORK AND PRESENTATIONS

Homework 1: Chapter 1: Exercises 1,2,6,7,11,12

Solutions to HW1 by Ryan Pellico

Homework 2: Chapter 2: Exercises 1,2,3,4,5,6

Chapter 1: Exercises 15,16

Solutions to HW2 by Mingfeng Zhao

Schedule of Presentations and Reports