By Hans Schoutens
Even with a few fresh purposes of ultraproducts in algebra, they continue to be mostly unknown to commutative algebraists, partly simply because they don't shield easy homes akin to Noetherianity. This paintings desires to make a powerful case opposed to those prejudices. extra accurately, it experiences ultraproducts of Noetherian neighborhood jewelry from a basically algebraic standpoint, 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 turn out asymptotic types 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 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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