By Hans Schoutens
Regardless of a few contemporary purposes of ultraproducts in algebra, they continue to be principally unknown to commutative algebraists, partially simply because they don't safeguard easy houses resembling Noetherianity. This paintings desires to make a robust case opposed to those prejudices. extra accurately, it experiences ultraproducts of Noetherian neighborhood earrings from a in simple terms algebraic point of view, in addition to how they are often used to move effects among the confident and 0 features, to derive uniform bounds, to outline tight closure in attribute 0, and to turn out asymptotic models of homological conjectures in combined attribute. a few of these effects are got utilizing versions known as chromatic items, that are frequently even Noetherian. This booklet, 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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