By Hans Schoutens
Regardless of a few contemporary functions of ultraproducts in algebra, they continue to be principally unknown to commutative algebraists, partially simply because they don't defend easy houses similar to Noetherianity. This paintings desires to make a powerful case opposed to those prejudices. extra accurately, it stories 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 turn out asymptotic models of homological conjectures in combined attribute. a few of these effects are got utilizing editions referred to 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 wish of popularizing ultraproducts and their purposes in algebra.
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