Titlebook: Commutative Algebra; with a View Toward A David Eisenbud Textbook 1995 Springer Science+Business Media New York 1995 Algebraic Geometry.alg

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https://doi.org/10.1057/9780230373136forth. The commutative algebra of codimension one is correspondingly rich. In this chapter we digress from the presentation of dimension theory and use the results of Chapters 9 and 10 to analyze some codimension-1 phenomena. In particular, we shall study “invertible” modules; give a criterion for a

lattice

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Studies in Soviet History and Society, how do the “fibers” . ?. .(.) vary as we vary the prime . of .? If . is flat over ., then as we have seen, there is some sense in which the fibers vary continuously. The main result below, Grothendieck’s generic freeness lemma, a consequence of the Noether normalization theorem, implies that if .

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Graduate Texts in Mathematicshttp://image.papertrans.cn/c/image/230751.jpg

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Wesley T. Huntress Jr.,Mikhail Ya. MarovIt has seemed to me for a long time that commutative algebra is best practiced with knowledge of the geometric ideas that played a great role in its formation: in short, with a view toward algebraic geometry.

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Wesley T. Huntress Jr.,Mikhail Ya. MarovFor the sake of establishing a common language, this chapter introduces some notation and elementary definitions such as would appear in many undergraduate algebra courses.

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Studies in Soviet History and SocietyWe shall work throughout this chapter with a polynomial ring . = .[., …, .] over a field .. The elements of . will be called .. All .-modules mentioned will be assumed finitely generated.

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IntroductionIt has seemed to me for a long time that commutative algebra is best practiced with knowledge of the geometric ideas that played a great role in its formation: in short, with a view toward algebraic geometry.

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