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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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A Brief History of Order Ideals,nd?”, has in fact encountered the concept of an order ideal. In the account on order ideals and their applications in this paper, it is our intent to elaborate on four basic theorems - as we see them - that give insight into the height properties of these ideals. We do this both from a historical view as well as a view of their utility.
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F-Purity, Frobenius Splitting, and Tight Closure,aded rings of positive prime characteristic when the normalization has an isolated singularity (or an isolated non-Cohen-Macaulay point), which includes all three-dimensional graded domains of positive characteristic. Applications of the closely related theory of tight closure are also discussed.
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Moduli of Abelian Varieties, Vinberg ,-Groups, and Free Resolutions,xamples and show how they are connected to moduli spaces of Abelian varieties. To make the article accessible to both algebraists and geometers, we also include background material on free resolutions and representation theory.
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Book 2013benefit of junior mathematicians and researchers who are new to the field; it  will aid them in broadening their background and to gain a deeper understanding of the current research in this area. Exciting developments are surveyed and many open problems are discussed with the aspiration to inspire the readers and foster further research..
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