Mathematics
250B
Spring, 2003
81 Evans
Hall, TuTh 12:402PM
885 Evans Hall
Office hours
Office telephone: 510 642 0648
Fax number:510 642 8204
Secretary:510 642 5026
email:
ribet@math.berkeley.edu
Textbook
Algebra
by
Serge Lang.
You want the
new edition
published by
SpringerVerlag
as volume number 211
in the
Graduate
Texts in Mathematics series.
This book is the classic algebra textbook
for graduate courses. I used an earlier edition when I was
an undergraduate at Brown University
and a graduate student at
Harvard.
You can look at some unofficial
companion
material
for Lang's
book that was written by
one
of
my
colleagues.
See, for instance, the
errata
to printings past and present.
Syllabus
According to the
Courseweb home page for this course, we should be covering
Tensor algebras and exterior algebras,
with application to linear transformations.
Commutative ideal theory, localization. Elementary specialization and
valuation theory. Related topics in algebra.
We will begin
with a study of linear and multilinear algebra and move on to study tensor
algebras and their quotients. There seems to be a big student interest
in commutative algebra, so that will come next.
In some sense, this course could be seen as a continuation
of the Math 250A course that I taught three
semesters ago.
I taught this course once before,
in 19921993.
You are welcome to consult the archive
for material from my old course, including the exams.
Note that
the course was taught
on Mondays, Wednesdays and Fridays, so the midterms were
only
50
minutes long.
Homework
Homework will be assigned weekly.
Problems will be graded by
John Voight,
the Graduate Student
Instructor assigned to this course.
John has set up his own
Math 250B
Course Web Page.

Assignment due January 30, 2003:
Chapter XIII, problems 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 16, 17, 18.
(This is a long list, but I like the problems. I removed only one or two
of them from my initial list.)

Assignment due February 6, 2003:
 Chapter XIII, problems 25, 26, 27, 28
 Chapter XIV, problems 3, 6, 8, 9, 13, 14, 15, 18, 20, 23

Assignment due February 13, 2003:
Chapter XVI, problems 6, 7, 8, 9, 12.
Also: let
R=k[x,y] be the
indicated polynomial ring in two variables over a field k. Show that
the maximal ideal (x,y) of R is not flat over R.

Problems due February 20, 2003:
 Chapter XIX, numbers 1, 2, 3, 4

Problems due March 6, 2003:
 Chapter X, numbers 18
 Find an example of an ideal I in an integral domain A for which there
is a prime in Ass(A/I) that is not in Ass(A).

Problems due Tuesday, March 18, 2003:

Chapter XVII, Exercises
1, 2, 3,
4, 5, 6, 7,
9,
10, 13

Problems due Tuesday, April 1, 2003:

Chapter XVII, Exercise 12 (just the first sentence, i.e., the "Prove that...")
 Chapter X, Exercises 9, 10, 11

Problems due Thursday, April 10, 2003:
Chapter VII, Exercises 1, 2, 4, 6, 7, 9, 10

The last homework assignment
is now available as a PDF document. Homework is due Friday,
May 16 at 4PM.
Kenneth A. Ribet
,
Math Department 3840, Berkeley CA 947203840