### Browse by Dr. Jingjing Ma is a department chair of Mathematics and Statistics and Professor of Mathematics at University of Houston-Clear Lake. Dr. Ma's 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 him.

### Recent Submissions

• #### Directed Partial Orderson Complex Numbers and Quaternions over Non-Archimedean Linearly Ordered Fields ﻿

(Order, 2016)
Let 'F' be a non-archimedean 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' ...
• #### Lattice-ordered matrix algebras containing positive cycles ﻿

(Positivity, 2013)
It is shown that if a lattice-ordered n × n (n ≥ 2) matrix ring over a totally ordered integral domain or division ring containing a positive n-cycle, then it is isomorphic to the lattice-ordered n × n matrix ring with ...
• #### Recognition of Lattice-ordered matrix algebras ﻿

(Order, 2013)
For an ℓ-unital ℓ-ring R, various recognition criteria are given for R to be isomorphic to a matrix ℓ-ring over an ℓ-unital ℓ-ring 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 d-rings ﻿

(Algebra Universe, 2014)
For an Archimedean d-ring 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 l-radical 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 l-Algebras over l-fields ﻿

(Cogent Mathematics, 2015)
It is shown that if a matrix ℓ-algebra Mn(K) over certain ℓ-fields K contains a positive n-cycle e such that I+e+⋯+en−1 is a d-element on K then it is isomorphic to the ℓ-algebra 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 non-archemedean totally ordered subfield of F with K+=F+∩K. In this note, directed partial orders are constructed for complex numbers ...