John A. Beachy
Professor Emeritus of Mathematical Sciences
Distinguished Teaching Professor
Department of Mathematical Sciences
Northern Illinois University
DeKalb, IL 60115
Department email: jbeachy(at)niu.edu
Department website: faculty.niu.edu/math_beachy/
Personal email: johnabeachy(at)gmail.com
NIU email
My books
Abstract Algebra, 4th Ed, Waveland Press (2019), co-authored with Bill Blair
Supplements (pdf): Selected Solutions for Students (62 pp, 2019) and A Study Guide for Beginners (224 pp, 2019)
Introductory Lectures on Rings and Modules, Cambridge University Press (1999)
Abstract Algebra: Study Guide, printed by CreateSpace, an Amazon.com company (2013)
Abstract Algebra, 3rd Ed, Waveland Press (2006), co-authored with Bill Blair
Supplements (pdf): A Study Guide for Beginners (203 pp, 2014), Review of Groups and Galois Theory (55 pp, 2007) and Selected Topics in Group Theory (25 pp, 2007)
Abstract Algebra, 2nd Ed, Waveland Press (1996), co-authored with Bill Blair
Abstract Algebra with a Concrete Introduction, Prentice-Hall (1990), co-authored with Bill Blair
My research
My research studies noncommutative rings, from the point of view of their categories of modules. I was introduced to this point of view by my doctoral advisor, Goro Azumaya. Some of my work has been to extend notions in the category of modules over a ring to the category subgenerated by a particular module.
Throughout my career I have been primarily interested in extending localization techniques from the commutative to the noncommutative case. One approach, essentially stemming from the work of Pierre Gabriel, studies injective modules and quotient categories. A second and rather different approach, initiated by P. M. Cohn, uses the universal localization at a prime ideal.
Copies (.pdf) of my papers can be found here.
MathSciNet at the NIU library
My personal interests
I have an interest in international education, since I graduated in 1960 from Woodstock School, located in north India in the foothills of the Himalaya. I attended Goshen College, which has an active foreign study program, and graduated in 1963. I completed my Ph.D. at Indiana University in 1967, and then taught for two years at Goshen College, before joining the Department of Mathematical Sciences at Northern Illinois University in 1969. Beside teaching at NIU for forty one years (I retired from teaching in 2010), I have been a visitor at McGill University, the University of London (Bedford College), the University of Washington (Math Department) and the University of Glasgow (Maths Department). My three daughters studied in the Dominican Republic, France, Senegal, Argentina, Mexico, and Costa Rica during college. Since my retirement, and before the pandemic, I typically spent several of the winter months at my “casita” near San Juan del Sur, Nicaragua. In 2021 I moved from DeKalb, Illinois, to Colorado Springs.
