John A. Beachy

Professor Emeritus of Mathematical Sciences
Distinguished Teaching Professor
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60115

office: Watson 359   |   telephone: (815) 753-0567   |   my departmental email address: jbeachy at

General information for math students

Courses I taught 2002 - 2010
These webpages usually include the syllabus, supplementary material, exams and quizzes (some with solutions), homework, etc.

For students using Abstract Algebra, 3rd Ed.:
            A Study Guide for Beginners (203 pages, pdf, posted 1/14/2014)
            Review of Groups and Galois Theory (55 pages, pdf, posted 1/11/2007)
            Selected Topics in Group Theory (25 pages, pdf, posted 1/12/2007)

For anyone still using Abstract Algebra, 2rd Ed.:
            OnLine Study Guide

Abstract Algebra OnLine

About my books

Introductory Lectures on Rings and Modules, Cambridge University Press
            Available online: Class Notes

Abstract Algebra, 3rd Ed, Waveland Press, co-authored with Bill Blair
            Available online: A Study Guide for Beginners
            Available online: Review of Groups and Galois Theory

Abstract Algebra: Study Guide, printed by CreateSpace, an company

Abstract Algebra, 2nd Ed, Waveland Press, co-authored with Bill Blair
            Available online: OnLine Study Guide

Abstract Algebra with a Concrete Introduction, Prentice-Hall, co-authored with Bill Blair

Research interests

My research studies noncommutative rings, from the point of view of their categories of modules. I am primarily interested in extending localization techniques from the commutative to the noncommutative case. One approach studies injective modules and quotient categories. A second and rather different approach uses the universal localization at a prime ideal.

Publications available in pdf format.   |   Complete list of publications

A list of ring theorists (from Allen Bell).

MathSciNet (at NIU libraries). Use Firefox and click on Databases: Core Databases

MathSciNet (at Rice University)

Personal interests

I have an interest in international education, since I graduated from Woodstock School (in 1960) and Goshen College (in 1963). I completed my Ph.D. at Indiana University (in 1967), and then taught for two years at Goshen College. In addition to teaching a NIU for forty one years (I retired from teaching in 2010), I have been a visitor at McGill University, University of London (Bedford College), the University of Washington (Math Dept), and the University of Glasgow (Math Dept). Since my retirement, I typically spend several of the winter months at my casita in Nicaragua.