I have published a number of papers in Mathematical Journals of repute and I continue to be actively involved in research on
Ring Theory being my main area of interest I briefly describe what kind of work I have been doing in it. In Ring Theory, I study:
- Commutative Ring Theory
- Partially Ordered Groups
- Elementary Number Theory
- Integral domains whose non-zero elements have some form of unique factorization
- Integral domains whose non-zero non-units are expressible as products of irreducible elements to see how far they are from being UFD's (Unique Factorization Domains)
- Generalizations of UFD's and Krull domains. Of these the most well-known are the weakly Krull and the weakly factorial domains. To see the impact of some of my work you may want to look up, " Ideal Systems, an introduction to Multiplicative Ideal Theory", by Franz Halter-Koch ISBN: 0-8247-0186-0.
- Subrings of polynomial rings over fields ( rings of the form A + XB[X] where AÍ B are subrings of a field K, X an indeterminate over K) to serve as examples.
- The notion of the divisor class group is restricted to domains that are completely integrally closed and it is mostly used in the context of Krull domains, I suggested the notion of a class group that is defined for any integral domain and that reduces to the divisor class group for Krull domains.
- A study of star operations.