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# Algebra

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 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. The index of a division algebra is the square root of the dimension of the algebra as a vector space over its center. One of the big open problems in the theory of division algebras is whether or not every division algebra of prime index can be described as a cyclic algebra, or equivalently, has a Galois maximal subfield. Prof. McKinnie has studied the existence of non-cyclic division algebras over a field with prime characteristic *p*, and index *pn*, *n*>1. She has also studied the existence of indecomposable division algebras with the same characteristics.

Recently Prof. McKinnie has worked with Profs. Eric Brussel of Emory University and Eduardo Tengan of ICMC, Brazil, to study the existence of non-cyclic and indecomposable division algebras over fields which are function fields of certain algebraic curves. She is very interested in using the techniques of algebraic geometry to solve problems in the theory of division algebras.

Professor **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.

## Emeritus Faculty

Professor **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.