Jingjing Ma
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Dr. Jingjing Ma is a department chair of Mathematics and Statistics and Professor of Mathematics at University of HoustonClear Lake. Dr. Ma's research interest is Latticeordered Rings and Algebras. G. Birkhoff and R.S. Pierce first established the general theory for latticeordered rings 50 years ago. But there is no good structure theory available for general latticeordered rings mainly because the condition connecting multiplication and lattice operations is too weak. Currently I am working on a class of latticeordered rings and algebras that contains some important examples in latticeordered rings such as latticeordered polynomial rings, latticeordered matrix and triangular matrix algebras, latticeordered 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 latticeordered rings and algebras. If you are interested in doing research in this direction or other problems in general latticeordered rings, please contact him.
Recent Submissions

Directed Partial Orderson Complex Numbers and Quaternions over NonArchimedean Linearly Ordered Fields
(Order, 2016)Let 'F' be a nonarchimedean linearly ordered field, and 'C' and 'H' be the field of complex numbers and the division algebra of quaternions over 'F', respectively. In this paper, a class of directed partial orders on 'C' ... 
Latticeordered matrix algebras containing positive cycles
(Positivity, 2013)It is shown that if a latticeordered n × n (n ≥ 2) matrix ring over a totally ordered integral domain or division ring containing a positive ncycle, then it is isomorphic to the latticeordered n × n matrix ring with ... 
Recognition of Latticeordered matrix algebras
(Order, 2013)For an ℓunital ℓring R, various recognition criteria are given for R to be isomorphic to a matrix ℓring over an ℓunital ℓring with the entrywise order. 
Lattice ordered matrix rings over totally ordered rings
(Order, 2014)For an nxn matric algebra over a totally ordered integral domain, necessary and sufficient conditions are derived such that the entrywise lattice order on it is the only lattice order (up to an isomorphism) to make it into ... 
Positive derivations on Archimedean drings
(Algebra Universe, 2014)For an Archimedean dring R and a positive derivation D on R it is shown that D(R) is a subset of N(R), where N(R) is the lradical of R. 
Directed partial orders on real quaternions
(Quaestioines Mathematicae, 2015)It is shown that a division ring of real quaternions can be made into a partially ordered ring with a directed partial order. 
Matrix lAlgebras over lfields
(Cogent Mathematics, 2015)It is shown that if a matrix ℓalgebra Mn(K) over certain ℓfields K contains a positive ncycle e such that I+e+⋯+en−1 is a delement on K then it is isomorphic to the ℓalgebra Mn(K) over K with the entrywise lattice order. 
Partial Orders on C=D + Di and H=D +Di +Dj + Dk
(International Journal of Advanced Mathematical Sciences, 2015)Let \(D\) be a totally ordered integral domain. We study partial orders on the rings \(C = D + Di\) and \(H = D + Di + Dj + Dk\), where \(i^{2} = j^{2} = k^{2} = 1\). 
Directed Partial Orders on Complex Numbers ad Quaternions II
(Positivity, 2015).Suppose that F is a partially ordered field with a directed partial order and K is a nonarchemedean totally ordered subfield of F with K+=F+∩K. In this note, directed partial orders are constructed for complex numbers ...