Concerning filtrations on commutative rings

Petro, John

doi:10.1007/bf01168678

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1975

1994

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Cited by 3 publications

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“…There exist (see [6]) simple examples of filtrations f which have δs power type r(f) any preassigned real number r > 1. There exist (see [6]) simple examples of filtrations f which have δs power type r(f) any preassigned real number r > 1.…”

Section: Lemma 2 21 Let F = {A N } Be a Filtration Which Satisfies mentioning

confidence: 99%

See 1 more Smart Citation

A theory of multiplicity for multiplictive filtrations.

1975

Journal Für Die Reine Und Angewandte Mathematik (Crelles Journal)

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A result in the theory of commutative rings [4], (21. 1) states that for a 0-dimensional ideal α in a noetherian ring A with identity and a finitely generated ^4-module M, the (cumulative) Hubert function L A (M/a n M) is a polynomial with rational coefficients for all sufficiently large n. This polynomial has degree at most s, the altitude of the ideal a. The multiplicity of M with respect to a is s! times the coefficient of the term of degree s and is frequently expressed by the limit formula of Samuel *) This research represents a portion of the author's doctoral dissertation at Western Michigan University.

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Section: Lemma 2 21 Let F = {A N } Be a Filtration Which Satisfies mentioning

confidence: 99%

“…2) and the intersection of two such filtrations need not be an AP-filtration [6]. 2) and the intersection of two such filtrations need not be an AP-filtration [6].…”

Section: Theorem 2 22 Let F = {A N } Be a Q-dimensional Filtration mentioning

confidence: 99%