My research revolves mostly around the theory of modules over arbitrary
associative rings with unity. I usually focus on injective or projective
modules and their generalizations such as continuous and discrete modules.
A great part of my work on recent years has been about the concepts of
extending (CS) modules, weak injectivity and weak projectivity. Weak injectivity
surfaced out of my work with S.K. Jain in 1988 studying rings whose cyclic
modules embed as essential submodules of projective modules. A module M
is said to be weakly injective if any finitely generated submodule of the
injective hull E(M) of M is contained in a submodule X of E(M) which is
isomorphic to M. The study of weak injectivity has connections with the
study of QI-rings, semiprime Goldie rings, q.f.d. rings, rings of quotients,
Algebraic Coding Theory continues to be an interesting topic for me. A paper on cyclic codes over the integers modulo p^n, written with Pramod Kanwar has recently been accepted for publication by Finite Fields and their applications. I am also working with Jeff Dill and others in our School of Electrical Engineering and Computer Science on several problems related to Trellis-Coded-Modulation systems.
Allen D. Bell from University of Wisconsin-Milwaukee is compiling a very nice list of ring theorists. I thought I would include a link to it here.