My principal fields of interest are Algebra and topology. In addition I also have developed some secondary interests in Algebraic Geometry, Ordered Sets, Finite Topologies and discrete Mathematics. My most work is devoted to some conjectures about chain conditions in polynomial rings and their localizations. My work focuses also on: pairs of rings where all intermediate rings satisfy a given ring theoretic property. Other interests include: Maximal non-P subrings, that I defined and published several papers on this topic. I have already published a paper on 2007 about digital topology (a branch of discrete mathematics) and the connectivity in digital topological spaces. Recently, I published some papers in discrete mathematics, including ordered sets, combinatorics and graph theory. Several results from my papers have been included in some recent books. Furthermore several of my papers have been cited by well known mathematicians in prestigious mathematics research journals. One of my papers was featured three times by The ScienceDirect Top 25 Hottest Articles. I have been invited to numerous conferences. Furthermore I have had several collaborators in my research.