*Introductory Lectures on Rings and Modules*

**by John A. Beachy**
London Mathematical Society Student Texts

Cambridge University Press, 1999,

ISBN 0-521-64340-6

Cambridge University Press,

Edinburgh Building,

Shaftesbury Road,

Cambridge CB2 2RU

## Supplementary Material

*Introductory Lectures on Rings and Modules:*

## SUPPLEMENT

From the preface to the supplement:

*The text
grew out of the first-year graduate course
that I have taught at Northern Illinois University.
In keeping with the noncommutative focus of the text,
I included a chapter on group representations
in place of the chapter on commutative rings
that is in our course syllabus.
Since a course at that level
should lay some foundation for later work in commutative algebra,
I felt that I should make my class notes available
as a supplement to the text.*

At this point,
the supplement is approximately 30 pages long
and includes the following sections.

**
Chapter 5: Commutative rings
**

**
**- 5.1 Primary decomposition
- 5.2 Noetherian rings
- 5.3 Dedekind domains
- 5.4 Integral extensions

**
**
I have labeled it a preliminary version,
because the notes refer to other sources for
the proofs of the Hilbert nullstellensatz
and the principal ideal theorem, among others.
I also intend to add further problems.
Please check back for a revised version.
The supplementary lecture notes are available to interested readers, in
**postscript**
or
**.pdf**
(Acrobat Reader) format.

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