# Hans Nordstrom | Research

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My research interested are primarily in noncommutative algebra and algebraic geometry.  In particular, I study associated primes and tosion thoery.  I have classified the associated primes of skew-polynomial modules over Ore extensions of the form $R[x;\sigma]$, where $\sigma$ is a surjective endomorphism of the base ring $R$.  My dissertation expands this result to generalized Weyl algebras.  Past work has also included representations of generalized Weyl algebras, $R[u,d; \sigma, q]$.  I am currently working on fundamental results on the structures of Leavitt path algebras (LPAs) built over arbitrary associative rings--including iterated LPAs.

#### Publications:

Associated Primes over Ore Extensions, J. Algebra, 286(1), 2005.  A .pdf is available here.

The genus level of a group, (with M. Arbo, K. Benkowski, B. Coate, C. Peterson & A. Wootton) Involve, 2 (3), 2009.  A .pdf is available here.

Simple Modules Over Generalized Weyl Algebras and Their Associated Primes, Comm. in Algebra, 40(9), 3224-3235.  A .pdf eprint is available here.  (There are 50 copies available; if you cannot access an eprint, please contact me for a copy.  HN)

#### Professional Talks/ Seminars:

Leavitt path algebras over arbitrary unital rings, 1073rd AMS meeting: Noncommutative Algebra, September 2011.

Torsion-theoretic representations of generalized Weyl algebras,
1041th AMS Meeting: Noncommutative Algebra and Geometry, October 2008.

Associated primes over generalized Weyl algebras, II,
1024th AMS Meeting: Noncommutative Algebra, March 2007.

Associated primes over generalized Weyl algebras, I,
PNWMAA Meeting: Junior Faculty Reserach, June 2006.

Associated Primes over Generalized Weyl Rings, 1012th
AMS Meeting: Special Session on Regular Algebras and Projective Geometry, November 2005.

Games, Graphs and other Tricks, Pacific University Mathematics Colloqium, April 2005

Associated Primes over Ore Extensions, Joint AMS/MAA Meetings: Number Theory III Contributed Paper Session, January 2005.

Prime Numbers, Prime Ideals, and Associated primes, Linfield College, Science Colloquium, Oct, 2004.

Generalizations of Primes in Noncommutative Algebra, University of Portland, Mathematics Colloquium, Oct. 6th, 2004.

Torsion Theories, University of Oregon, Ring Theory Seminar, May 25th, 2004.

Associated Primes over Ore Extensions I, University of Oregon, Ring Theory Seminar, Feb. 10th, 2004.

Associated primes over Skew-Polynomial Rings II, University of Oregon, Ring Theory Seminar, Nov. 18th, 2003.

Some Theorems on Cubic Plane Curves, University of Oregon, Ring Theory Seminar, May 27th, 2003.

Associated Primes over Skew-Polynomial Rings, University of Oregon, Ring Theory Seminar, Nov 5th, 2002.

Linking Prime Ideals, University of Oregon, Ring Theory Seminar, May 21st, 2002.

Goldie Rings and the Three Bears, University of Oregon, Ring Theory Seminar, April 30th, 2002.

A Festival of Prime Ideals, University of Oregon, Ring Theory Seminar, Nov. 6th, 2001.