Former Ralph and Jean Storm Professor of Mathematics
Ralph and Jean Storm Professor Emeritus of Mathematics
Ph.D., Univ. of Illinois, Urbana, 1969 (Advisor: J. Rotman)
M.A., Western Washington State, 1965
Dr. Arnold joined the Baylor faculty as the Ralph and Jean Storm Professor of Mathematics in the fall of 1990. Previously, he served as post-doctoral fellow and professor of mathematics at New Mexico State University. In addition, he has been a visiting professor of mathematics and taught classes and seminars at the University of Washington, University of Connecticut, University of Essen (Germany), and Florida Atlantic University.
1. Undergraduate and graduate algebra, both pure and applied.
2. Undergraduate discrete mathematics, including error-correcting codes and cryptography.
3. Mathematics for liberal arts students, including an original sources honor course and connections between mathematics and music.
Academic Interests and Research:
Dr. Arnold's research is in torsion-free abelian groups of finite rank and related subjects, such as representation of finite partially ordered sets, modules over discrete valuation rings, subrings of algebraic number fields, and finitely generated modules over pullback rings.
1. Finite Rank Torsion-free Abelian Groups and Rings, Lecture Notes in Mathematics 931, Springer-Verlag, New York, 1982, 191 pp.
2. Abelian Groups and Representations of Partially Ordered Sets, CMS Advanced Books in Mathematics, Springer-Verlag, New York, 2000, 244 pp.
3. Co-editor: Abelian Group Theory, Lecture Notes in Mathematics, 616, Springer-Verlag, New York, 1977, 423 pp.
4. Co-editor: Abelian Groups and Modules, Pure and Applied Math., Marcel Dekker, New York, 1996, 411 pp.
5. Co-editor: Abelian Groups and Modules, Proceedings of 2001 Honolulu Conference on Abelian Groups and Modules, Rocky Mountain Journal of Mathematics, Vol. 3, Winter, 2002, 610 pp.
Selected Research Articles:
1. Almost completely decomposable groups and unbounded representation type, J. Alg. 349 (2012), 50-62 (with A. Mader, O. Mutzbauer, E. Solak).
2. Indecomposable (1,3)-groups and a matrix problem, Czech Math. J. 63 (2013), 307-355 (with A. Mader, O. Mutzbauer, E. Solak).
3. Locally free abelian groups of finite rank, Contributions to Module Theory: In Memory of A.L.S. Corner, de Gruyter Press, 2008, 83-97.
4. Subgroups of finite direct sums of Z[1/n], Houston J. Math., 34 (2008), 997-1008.
5. Representations of finite partially ordered sets over commutative artinian uniserial rings, J. Pure and Appl. Alg. 205 (2006), 640-659 (with D. Simson).
6. Endo-wild representation type and generic representations of finite posets, Pacific J. Math. 219 (2005), 101-126 (with D. Simson).