By Hans Schoutens

In spite of a few contemporary purposes of ultraproducts in algebra, they continue to be principally unknown to commutative algebraists, partially simply because they don't defend uncomplicated homes akin to Noetherianity. This paintings desires to make a robust case opposed to those prejudices. extra accurately, it reports ultraproducts of Noetherian neighborhood jewelry from a only algebraic point of view, in addition to how they are often used to move effects among the confident and nil 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 acquired 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 wish of popularizing ultraproducts and their purposes in algebra.

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