Education
The University of Toledo, Toledo, Ohio, USA.
- Ph.D. in Mathematics - 1999
- M.A.
in Mathematics - 1996
Research Interests
My research interest is in Partially ordered rings and algebras, and lattice-ordered rings and algebras.
G. Birkhoff and R.S. Pierce first established the general theory for lattice-ordered
rings in 1956. My focus is getting better understanding of the structures of partially ordered and lattice-ordered rings and algebras, and answering open questions in partially ordered and lattice-ordered rings and algebras.
Recently, I answered an open question posted in the paper "Fields with directed partial orders, J. Algebra, 336 (2011), 342-348" by N. Schwartz and Y. Yang, where the authers state that "It remains an open question whether non-real algebraic number fields carry a directed partial orders". I provided a nagetive answer to the question by using the theory of infinite primes for rings and fields developed by Harrison around 1960.