Mathematical Sciences: Rings of Finite Global Dimension

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This project is concerned with rings of finite global dimension, particularly classical orders over a commutative discrete valuation ring and related Artinian rings of finite global dimension. The principal investigator will consider the problem of obtaining an upper bound on the global dimension of Noetherian PI rings which have finite global dimension. The structure of orders and Artin algebras of finite global dimension will also be studied. This will be useful in attacking Tarsy's conjecture. This project is in the general area of ring theory. It is concerned with the global dimension of a class of rings. The global dimension measures certain properties of a ring. This research will try to determine if there is an upper bound on this measurement for a restricted class of rings.