Mathematical Sciences: Non-commutative Ring Theory

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This project is concerned with noetherian rings and rings satisfying a polynomial identity. The relationship between certain homological dimensions and the classical Krull dimension of various noetherian rings will be considered. The embedding of noetherian rings into artinian rings will be examined in the light of recent results about Sylvester rank functions. The principal investigator will also study Gelfand-Kirillov dimension. Ring theory concerns algebraic structures having both an addition and multiplication of their elements. These structures occur throughout algebra and analysis. This project is concerned with measuring certain aspects of classes of rings.