Download E-books The Use of Ultraproducts in Commutative Algebra (Lecture Notes in Mathematics) PDF

By Hans Schoutens

Regardless of a few fresh purposes of ultraproducts in algebra, they continue to be mostly unknown to commutative algebraists, partially simply because they don't look after uncomplicated homes akin to Noetherianity. This paintings desires to make a powerful case opposed to those prejudices. extra accurately, it experiences ultraproducts of Noetherian neighborhood earrings from a only algebraic viewpoint, in addition to how they are often used to move effects among the optimistic and 0 features, to derive uniform bounds, to outline tight closure in attribute 0, and to end up asymptotic models of homological conjectures in combined attribute. a few of these effects are received utilizing editions known as chromatic items, that are frequently even Noetherian. This ebook, neither assuming nor utilizing any logical formalism, is meant for algebraists and geometers, within the desire of popularizing ultraproducts and their functions in algebra.

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