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Flatness

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The Use of Ultraproducts in Commutative Algebra

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1999))

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Abstract

To effectively apply ultraproducts to commutative algebra, we will use, as our main tool, flatness. Since it is neither as intuitive nor as transparent as many other concepts from commutative algebra, we review quickly some basic facts, and then discuss some flatness criteria that will be used later on. Flatness is an extremely important and versatile property, which underlies many deeper results in commutative algebra and algebraic geometry. In fact, I dare say that many a theorem or conjecture in commutative algebra can be recast as a certain flatness result; an instance is Proposition 6.4.6. With David Mumford, the great geometer, we observe:

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Authors and Affiliations

  1. Department of Mathematics, City University of New York CUNY Graduate Center, 365 Fifth Avenue, New York, NY, 10016, USA

    Hans Schoutens

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  1. Hans Schoutens
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Correspondence to Hans Schoutens .

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Schoutens, H. (2010). Flatness. In: The Use of Ultraproducts in Commutative Algebra. Lecture Notes in Mathematics(), vol 1999. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13368-8_3

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