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Algebra
The department's algebra group consists of two tenure-track faculty members, Kelly McKinnie and Nikolaus Vonessen, and two emeritus professors, William Ballard and Gloria C. Hewitt.

In a typical semester, we offer both an undergraduate and a graduate course in algebra, as well as the algebra seminar. In it, both faculty and graduate students give series of 2 to 4 lectures on a variety of advanced topics. Besides introducing graduate students to many interesting subjects, this seminar provides valuable experience in exposition.
Faculty
Associate Professor Kelly McKinnie received her Ph.D. from the University of Texas in 2006. She then completed post-doctoral appointments at Emory University in Atlanta, GA and Rice University in Houston, Texas before joining the department of mathematical sciences at the University of Montana in Fall 2009. Her general research interests include finite dimensional division algebras, the Brauer group, valuation theory, and algebraic geometry. Dr. McKinnie's has recently published papers on cyclicity in division algebras, Brauer dimension of fields and indecomposability of division algebras. Dr. McKinnie is also active in mathematical outreach for middle and high school students. She has applied for and received grants from the Dolciani Education Foundation through the MAA to establish "Math Day" a yearly event at the University of Montana, and "Math Beyond the Classroom" an outreach program for talented middle and high school math students.

Prof. Nikolaus Vonessen received his Ph.D. from MIT in 1988. His general research interests lie in ring theory, division algebras, and invariant theory. Much progress has been made in recent decades in understanding the structure of noncommutative rings and algebras. This makes it possible to study group actions and related invariant-theoretic questions in this setting. Prof. Vonessen's work in this direction is based on two different developments: first on the deep and well-understood commutative invariant theory, classical and geometric; and second, on the theory of finite group actions on noncommutative rings, which attracted much attention during the seventies and early eighties. In his research, he has been primarily concerned with actions of linear algebraic groups; one can call this area of research noncommutative invariant theory.

In recent years he has also studied, together with Prof. Zinovy Reichstein of the University of British Columbia, division algebras, and actions of algebraic groups on division algebras and central simple algebras.
Emeritus Faculty
Prof. William Ballard received his Ph.D. from the University of Chicago in 1957.  His interests lie in associative algebra.

Prof. Gloria C. Hewitt received her Ph.D. from the University of Washington in 1962. She is interested in generalized Noetherian rings. Prof. Hewitt was chair of the Department of Mathematical Sciences, and served on the board of directors of the National Association of Mathematicians.
Mathematical Sciences | University of Montana