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Titlebook: Commutative Algebra; Expository Papers De Irena Peeva Book 2013 Springer Science+Business Media New York 2013 Castelnuovo-Mumford regularit

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F-Purity, Frobenius Splitting, and Tight Closure,scussed. These include some problems that, historically, motivated the development of the theory. One of these is the theorem that rings of invariants of linearly reductive groups acting on regular rings are Cohen-Macaulay, including normal rings generated by monomials. Another is the characterizati
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Bounding Projective Dimension,bound on the projective dimension of J depending only on the number of elements in a minimal system of homogenoeus generators of J and their degrees (in particular, independent of the number of variables)?
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