On a study of Hilbert functions and Betti numbers of Artinian Gorenstein graded algebras
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| File | |
| Title ( eng ) |
On a study of Hilbert functions and Betti numbers of Artinian Gorenstein graded algebras
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| Title ( jpn ) |
アルティン・ゴレンスタイン次数付代数のヒルベルト関数とベッチ数列の研究
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| Creator |
Harima Tadahito
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| Descriptions |
Contents
1 Introduction / p1 1-1 Hilbert functions and Betti numbers / p1 1-2 Characterization of possible Hilbert functions and Betti numbers / p3 1-3 Main results / p5 2 Preliminaries / p8 2-1 Some standard facts of linkage theory / p8 2-2 Some basic properties of Hilbert functions / p9 3 Some examples of unimodal Gorenstein sequences / p11 3-1 Hilbert functions of certain Gorenstein algebras / p11 3-2 Gorenstein sequences of codimension three / p14 3-3 Unimodal Gorenstein sequences of codimension four / p17 4 Artinian Gorenstein algebras with the weak Stanley property / p20 4-1 A construction of a number of Artinian Gorenstein algebras with the weak Stanley property / p20 4-2 A characterization of Hilbert functions of Artinian Gorenstein algebras with the weak Stanley property / p23 5 Artinian Gorenstein algebras of codimension three / p25 5-1 The possible diagonal degrees / p25 5-2 A construction of Artinian Gorenstein algebras achieving all possible Betti numbers for codimension three / p26 5-3 Artinian Gorenstein algebras defined by the saturated diagonal degrees / p32 References / p37 |
| NDC |
Mathematics [ 410 ]
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| Language |
eng
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| Resource Type | doctoral thesis |
| Rights |
Copyright(c) by Author
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| Publish Type | Not Applicable (or Unknown) |
| Access Rights | open access |
| Source Identifier |
1) T. HARIMA, Some examples of unimodal Gorenstein sequences, Journal of Pure and Applied Algebra, Vol.103 (1995) 313-324.
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2) T. HARIMA, Characterization of Hilbert functions of Gorenstein Artin algebras with the weak Stanley property, Proceedings of the American Mathematical Society, Vol.123 (1995) 3631-3638.
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3) T. HARIMA, A note on Artinian Gorenstein algebras of codimension three, Journal of Pure and Applied Algebra, Vol.135 (1999) 45-56.
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[DOI] http://dx.doi.org/10.1016/0022-4049(95)00109-A
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[URI] http://www.jstor.org/stable/2161887
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[DOI] http://dx.doi.org/10.1016/S0022-4049(97)00162-X
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| Dissertation Number | 乙第3060号 |
| Degree Name | |
| Date of Granted | 1998-03-05 |
| Degree Grantors |
広島大学
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