On a study of Hilbert functions and Betti numbers of Artinian Gorenstein graded algebras
この文献の参照には次のURLをご利用ください : http://doi.org/10.11501/3147842
| ID | 33817 |
| 本文ファイル | |
| 別タイトル | 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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| 著者 |
張間 忠人
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| NDC |
数学
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| 目次 | 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 |
| SelfDOI | |
| 言語 |
英語
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| NII資源タイプ |
学位論文
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| 広大資料タイプ |
学位論文
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| DCMIタイプ | text
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| フォーマット | application/pdf
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| 著者版フラグ | ETD
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| 権利情報 | Copyright(c) by Author
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| 関連情報(references) | 1) T. HARIMA, Some examples of unimodal Gorenstein sequences, Journal of Pure and Applied Algebra, Vol.103 (1995) 313-324.
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.
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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| 関連情報URL(references) | http://dx.doi.org/10.1016/0022-4049(95)00109-A
http://www.jstor.org/stable/2161887
http://dx.doi.org/10.1016/S0022-4049(97)00162-X
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| 学位記番号 | 乙第3060号
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| 授与大学 | 広島大学(Hiroshima University)
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| 学位名 | 博士(理学)
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| 学位名の英名 | Physical Science
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| 学位の種類の英名 | doctoral
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| 学位授与年月日 | 1998-03-05
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| 部局名 |
理学研究科
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