Flatness

Abstract

AbstractTo 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:KeywordsExact SequencePrime IdealLocal RingShort Exact SequenceNoetherian RingThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.