Jingjing Ma, Ph.D.
Department Chair of Mathematics and Statistics and Professor of Mathematics,
College of Science and Engineering
Tuesday & Thursday
- Lecture Notes On Algebraic Structure of Lattice-Ordered Rings, World Scientific Publishing 2014. (http://www.worldscientific.com/worldscibooks/10.1142/9009) Correction and Addition
- (36) J. Ma, L. Wu, Y. Zhang, Directed partial orders on complex numbers and quaternions over non-archimedean linearly ordered fields, Order (2016) (published online first: 3/5/2016).
- (35) J. Ma, Directed partial orders on complex numbers and quaternions II, Positivity (2015) (published online first: 12/07/2015).
- (34) J. Ma, Partial orders on C = D + Di and H = D + Di + Dj + Dk, International Journal of Advanced Mathematical Sciences, 3 (2) (2015), 156-160.
- (33) J. Ma, Matrix l-algebras over l-fields, Cogent Mathematics 2 (2015) (published online first, 6/15/2015).
- (32) J. Ma, Directed partial orders on real quaternions, Quaestiones Mathematicae (2015) (12/14/2015 published online first).
- (31) J. Ma, Y. Zhang, Positive derivations on Archimedean d-rings, Algebra Univers. 72 (2014), 163-166.
- (30) J. Ma, Y. Zhang, Lattice-ordered matrix rings over totally ordered rings, Order 31 (2014), 45-54.
- (29) J. Ma, Recognition of Lattice-ordered matrix algebras, Order 30 (2013), 617-623.
- (28) J. Ma, Y. Zhang, Lattice-ordered matrix algebras containing positive cycles, Positivity 17 (2013), 299-307.
Courses (Current Academic Year)
MATH 3300: Introduction to Modern Algebra and Number Theory, MW 5:30-6:50pm, B1135.
Book: Discrete Mathematics with Applications, by S. Epp, fourth edition.
MATH 4322: Introduction to Abstract Algebra, TTh 4:00-5:20pm, B1104.
Book: Modern Algebra: An Introduction, by J. Durbin, sixth edition.
MATH 5133: Complex Analysis, MW 7:00-8:20pm, B3315.
Book: Complex Variables and Applications, by J. Brown and R. Churchill, eighth edition.
My research interest is Lattice-ordered Rings and Algebras.
G. Birkhoff and R.S. Pierce first established the general theory for lattice-ordered rings 50 years ago. But there is no good structure theory available for general lattice-ordered rings mainly because the condition connecting multiplication and lattice operations is too weak. Currently I am working on a class of lattice-ordered rings and algebras that contains some important examples in lattice-ordered rings such as lattice-ordered polynomial rings, lattice-ordered matrix and triangular matrix algebras, lattice-ordered group and twisted group algebras, all with standard lattice orders. Those examples are faraway from being f -rings. A general good structure theory is expected to obtain for this class of lattice-ordered rings and algebras. If you are interested in doing research in this direction or other problems in general lattice-ordered rings, please contact me.