Jeremy Edison, Ph.D.
Assistant Professor
- Milwaukee WI UNITED STATES
Dr. Edison specializes in algebra, linear algebra and mathematical education.
Education, Licensure and Certification
Ph.D.
Mathematics
University of Iowa
2019
M.S.
Mathematics
University of Iowa
2016
B.A.
Mathematics
Knox College
2014
Biography
His scholarly work examines invertible algebras, Ore extensions and triangularization of operator algebras on infinite-dimensional vector spaces. His research has appeared in the Journal of Algebra and has included collaborations with Miodrag C. Iovanov and Alexander Sistko.
Edison also has experience in mathematics education and interdisciplinary academic initiatives. Before joining Milwaukee School of Engineering, he served in mathematics faculty and leadership roles at Mount Mary University, where his work included mathematical instruction, faculty collaboration and initiatives addressing math anxiety.
He earned a Bachelor of Arts from Knox College and a Master of Science and Ph.D. from the University of Iowa.
Areas of Expertise
Accomplishments
Outstanding Teaching Assistant Award, University of Iowa Council on Teaching
2017
Ada Louise Ballard and Seashore Dissertation Fellowship
2019
Kappa Mu Epsilon, Mount Mary University
2020
Event and Speaking Appearances
Insights from a Math Anxiety Interventions Workshop
MAA MathFest 2024 Indianapolis, IN
Selected Publications
Ore extensions and infinite triangularization
Journal of AlgebraJeremy R. Edison, Miodrag C. Iovanov, Alexander Harris Sistko
2020-12-28
We give infinite triangularization and strict triangularization results for algebras of operators on infinite-dimensional vector spaces. We introduce a class of algebras we call Ore-solvable algebras: these are similar to iterated Ore extensions but need not be free as modules over the intermediate subrings. Ore-solvable algebras include many examples as particular cases, such as group algebras of polycyclic groups or finite solvable groups, enveloping algebras of solvable Lie algebras, quantum planes and quantum matrices. We prove both triangularization and strict triangularization results for this class, and show how they generalize and extend classical simultaneous triangularization results such as the Lie and Engel theorems.
On invertible algebras
Journal of AlgebraJeremy R. Edison, Miodrag C. Iovanov
2019-07-12
An algebra A over a field K is said to be invertible if it has a basis ℬ consisting only of units; if ℬ−1 is again a basis, A is invertible-2, or I2. The question of when an invertible algebra is necessarily I2 arises naturally. The study of these algebras was recently initiated by López-Permouth, Moore, Szabo, Pilewski [13], [14]. In this paper, we prove several positive results on this problem, answering also some questions and generalizing a few results from these papers. We show that every field is an I2 algebra over any subfield, and that any subalgebra of the rational functions field
