Mathematical Sciences: Non-commutative Rings

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This research is concerned with non-commutative ring theory. The principal investigator will apply algebraic K-theory and cyclic homology to the study of group rings and crossed products. In addition, he will investigate special dimension functions in ring theory with particular emphasis on global dimension and Gelfand-Kirillov dimension. A ring is an algebraic object having both an addition and a multiplication defined on it. These structures arise naturally in many different settings and are of interest in mathematics, computer science, engineering and physics.