By Hans Schoutens
Inspite of a few fresh functions of ultraproducts in algebra, they continue to be mostly unknown to commutative algebraists, partially simply because they don't defend easy houses similar 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 in basic terms algebraic point of view, in addition to how they are often used to move effects among the optimistic and nil features, to derive uniform bounds, to outline tight closure in attribute 0, and to turn out asymptotic types of homological conjectures in combined attribute. a few of these effects are acquired utilizing editions known as chromatic items, that are usually 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 purposes in algebra.
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