Publications

Mathematical Research Publications

1. The Henselization of a valued division algebra, J. Algebra 122 (1989), 232-243.
2. Value functions on central simple algebras, Trans. Amer. Math. Soc. 315 (1989), 605-622.
3. Integral Dubrovin valuation rings (with A. Wadsworth), Trans. Amer. Math. Soc. 315 (1989), 623-640.
4. Baer orderings with noninvariant valuation ring (with A. Wadsworth), Israel J. Math. 68 (1989), 241-255.
5. An approximation theorem for Dubrovin valuation rings, M. Zeit. 207 (1991), 71-82.
6. On Dubrovin valuation rings in crossed product algebras (with D. Haile), Trans. Amer. Math. Soc. 338 (1993), 723-752.
7. Maximal orders over valuation rings, J. Algebra 152 (1992), 313-341.
8. Noncommutative Prüfer rings satisfying a polynomial identity, J. Algebra 161 (1993), 324-341.
9. Bézout orders and Henselization (with D. Haile and A. Wadsworth), J. Algebra 173 (1995), 394-423.
10. On defective division algebras, pp. 359-367 in "K-Theory and Algebraic Geometry: Connections with Quadratic Forms and Division Algebras'', (eds. B. Jacob and A. Rosenberg), Proc. Symp. Pure Math., Vol. 58, Part 2, Amer. Math. Soc., Providence, R.I., 1995.
11. Kummer subfields of tame division algebras (with B. A. Sethuraman), J. Algebra 172 (No. 2) (1995), 554-583.
12. Indecomposable division algebras with a Baer ordering (with B.A. Sethuraman), Comm. Alg. 22 (1994), 5401-5418.
13. Noncrossed product division algebras with a Baer ordering (with B. A. Sethuraman), Proc. Amer. Math. Soc. 123 (1995), 1995-2003.
14. Divisors on division algebras and error correcting codes (with B. A. Sethuraman), Comm. Alg. 26 (1998), 3211-3221.
15. Lie algebras, composition algebras, and the existence of cross products on finite dimensional vector spaces, Expo. Math 17 (1999), 63-73.
16. Decomposition of Involutions on Inertially Split Division Algebras (with B. A. Sethuraman), Math. Z. 235 (No. 1) (2000), 195-212.
17. Generalized Cocycles with Values in One-Units of Henselian Valued Division Algebras (with B. A. Sethuraman), J. Algebra 224 (2000), 123-139.
18. On the Tensor Product of Composition Algebras (with J-M Perez-Isquierdo and S. Pumplün), J. Algebra 243 (2001), 41-68.
19. Hyperbolicity of algebras with involution and connections with Clifford algebras (with D. Haile), Comm. Alg 29 (2001), 5733-5753.
20. The Priestley Separation Axiom for Scattered Spaces (with G. Bezhanishvili and R. Mines), Order 19 (2002), 1-10.
21. Scattered, Hausdorff-Reducible, and Hereditarily Irresolvable Spaces (with G. Bezhanishvili and R. Mines), Topology Appl. 132 (2003), 291-306.
22. Division algebras with an anti-automorphism but with no involution (with B.A. Sethuraman and J.-P. Tignol), Advances in Geometry 5 (2005), 485-495.
23. Valuations on tensor powers of a division algebra (with B.A. Sethuraman), Journal of Algebra 293 (2005), 385-394.

1. Calculus instruction at New Mexico State University through weekly themes and cooperative learning (with J. Alvarez, D. Finston and M. Gehrke), Primus 3 (1993), 83-98.
2. Exploration, explanation, formalization: a three-step approach to proof (with T. Hodgson), Primus 6 (1996), 49-58.
3. Computing the Symmetry Groups of the Platonic Solids with the Help of Maple, Resonance 9 (8) (2004), 18-26.

1. Field and Galois Theory, Graduate Texts in Mathematics, Vol. 167, Springer-Verlag, New York, 1996.
2. Mathematics Courses using Themes (with J. Alvarez, M. Gehrke, D. Kurtz, R. Staffeldt), unpublished manuscript.