Publications

Items whose names start with a year are published.

Lattice Theory/Topology Papers

  1. Modal operators on rings of continuous functions (with G. Bezhanishvili and L. Carai)
  2. Free bounded archimedean l-algebras (with G. Bezhanishvili and L. Carai)
  3.  Coalgebras for the powerset functor and Thomason duality (with G. Bezhanishvili and L. Carai)
  4. A new approach to the Katetov-Tong theorem (with G. Bezhanishviliand B. Olberding)
  5. 2020 Gelfand-Naimark-Stone duality for normal spaces and insertion theorems (with G. Bezhanishvili and B. Olberding)
  6. 2020 A generalization of Gelfand-Naimark-Stone duality to completely regular spaces (with G. Bezhanishvili and B. Olberding)
  7. 2020 The frame of nuclei of an Alexandroff space (with F. Ávila, G. Bezhanishvili and A. Zaldívar)
  8. 2020 When is the frame of nuclei spatial: a new approach (with F. Ávila, G. Bezhanishvili and A. Zaldívar)
  9. 2020 Specker Algebras: A Survey (with G. Bezhanishvili and B. Olberding)
  10. 2019 An extension of de Vries duality to normal spaces and locally compact Hausdorff spaces (with G. Bezhanishvili and B. Olberding)
  11. 2019 An extension of de Vries duality to completely regular spaces and compactifications (with G. Bezhanishvili and B. Olberding)
  12. 2018 Canonical extensions of bounded archimedean vector lattices (with G. Bezhanishvili and B. Olberding)
  13. 2017 Proximity biframes and Nachbin spaces (with G. Bezhanishvili)
  14. 2017 Pierce sheaves and commutative idempotent generated algebras (with G. Bezhanishvili and B. Olberding)
  15. 2016 A functorial approach to Dedekind Completions and the representation of vector lattices and l-algebras by normal functions (with G. Bezhanishvili and B. Olberding)
  16. 2015 Proximity biframes and compactifications of completely regular ordered spaces (with G. Bezhanishvili)
  17. 2015 Profinite Topological Spaces (with G. Bezhanishvili, D. Gabalaia, and M. Jibladze)
  18. 2015 De Vries powers: a generalization of Boolean powers for compact Hausdorff spaces (with G. Bezhanishvili, V. Marra, and B. Olberding)
  19. 2015 Idempotent generated algebras and Boolean powers of commutative rings (with G. Bezhanishvili, V. Marra, and B. Olberding)
  20. 2013 Dedekind Completions of bounded archimedean l-algebras (with G. Bezhanishvili and B. Olberding)
  21. 2013 Bounded Archimedean l-algebras and Gelfand-Neumark-Stone duality (with G. Bezhanishvili and B. Olberding)
  22. 2011 Order-Compactifications of Totally Ordered Spaces (with G. Bezhanishvili)
  23. 2011 One-point order compactifications (with G. Bezhanishvili)
  24. 2010 Scattered and hereditarily irresolvable spaces in modal logic (with G. Bezhanishvili)
  25. 2010 Priestley rings and Priestley order-compactifications(with G. Bezhanishvili)
  26. 2009 Profinite Heyting algebras and profinite completions of Heyting algebras (with G. Bezhanishvili)
  27. 2007 Topo-canonical completions of closure algebras and Heyting algebras (with G. Bezhanisvhili and R. Mines)
  28. 2006 Profinite completions and canonical extensions of Heyting algebras (with G. Bezhanisvhili, M. Gehrke, and R. Mines)
  29. 2003 Scattered, Hausdorff-reducible, and hereditarily irresolvable spaces (with G. Bezhanisvhili and R. Mines)
  30. 2002 The Priestley separation axiom for scattered spaces (with G. Bezhanisvhili and R. Mines)

Division Algebra Papers

  1. 2006 A Springer theorem for higher degree forms
  2. 2005 Division algbras with an anti-automorphism but with no involution (with B. A. Sethuraman and J.-P. Tignol)
  3. 2005 Valuations on tensor powers of a division algebra (with B. A. Sethuraman)
  4. 2001 Hyperbolicity of algebras with involution and connection with Clifford algebras (with D. Haile)
  5. 2001 On the tensor product of composition algebras (with J. M. Pérez-Izquierdo and S. Pumplün)
  6. 2000 Generalized cocycles with values in one-units of Henselian valued division algbras (with B. A. Sethuraman)
  7. 2000 Decomposition of involutions on inertially split division algebras (with B. A. Sethuraman)
  8. 1999 Lie algebras, composition algebras, and the existence of cross products on finite-dimensional vector spaces
  9. 1998 Divisors on division algebras and error correcting codes (with B. A. Sethuraman)
  10. 1995 Noncrossed product division algebras with a Baer ordering (with B. A. Sethuraman)
  11. 1995 Kummer subfields of tame division algebras (with B. A. Sethuraman)
  12. 1995 Bezout orders and Henselization (with D. Haile and A. Wadsworth)
  13. 1995 On defective division algebras
  14. 1993 On Dubrovin valuation rings in crossed product algebras (with D. Haile)
  15. 1994 Indecomposable division algebras with a Baer ordering (with B. A. Sethuraman)
  16. 1993 Noncommutative Prufer rings satisfying a polynomial identity
  17. 1992 Maximal orders over valuation rings
  18. 1991 An approximation Theorem for Dubrovin valuation rings
  19. 1989 Baer orderings with noninvariant valuation ring (with A. Wadsworth)
  20. 1989 Integral Dubrovin valuation rings (with A. Wadsworth)
  21. 1989 Value functions on central simple algebras
  22. 1989 The Henselization of a valued division algebra

Books

  1. 2010 Abstract Algebra: Structure and Application (with D. Finston)
  2. 1996 Field and Galois Theory

Education Papers

  1. 2013 Feedback to support learning in the leadership institute for teachers (with J. Bradley and K. Kinzer)
  2. 2004 Computing the symmetry groups of the Platonic solids with the help of Maple
  3. 1996 Exploration explanation formalization a three-step approach to proof (with T. Hodgson)
  4. 1993 Calculus instruction at New Mexico State University through weekly themes and cooperative
    learning
    (with J. Alvarez, D. Finston, and M. Gehrke)