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:


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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