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Powers of ideals having small analytic deviation. (English) Zbl 0758.13001
The analytic spread \(\ell(I)\) of an ideal \(I\) of a Noetherian local ring \((R,M)\) with infinite residue field is defined as the Krull dimension of the graded ring \(\bigoplus^ \infty_{i=0}(I^ i/MI^ i)\) and \(\ell(I)-ht(I)\) is said to be the analytic deviation of \(I\). The paper is devoted to a detailed study of ideals in Cohen-Macaulay local rings having analytic deviations one or two. In the last part of the paper some illustrative examples and applications are presented.
Reviewer: L.Bican (Praha)

13A30 Associated graded rings of ideals (Rees ring, form ring), analytic spread and related topics
13H10 Special types (Cohen-Macaulay, Gorenstein, Buchsbaum, etc.)
13A15 Ideals and multiplicative ideal theory in commutative rings
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