Mathematical Sciences: Noncommutative Rings

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This project is concerned with problems in noncommutative ring theory, category theory and other areas of algebra. The principal investigator will work on representable functors from varieties of associative rings to varieties of other algebraic objects. In addition, he will study the Gel'fand-Kirillov dimension of factor rings and lattices realizable as lattices of all two-sided ideals of von Neumann regular rings. The research supported concerns a wide spectum of problems in ring theory. It has the potential of impacting many areas of mathematics including ring theory, algebraic number theory, finite group theory and universal algebra, as well as, computer science.