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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28545完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 朱樺 | |
| dc.contributor.author | Hsiang-Chun Hsu | en |
| dc.contributor.author | 徐祥峻 | zh_TW |
| dc.date.accessioned | 2021-06-13T00:11:38Z | - |
| dc.date.available | 2007-07-31 | |
| dc.date.copyright | 2007-07-31 | |
| dc.date.issued | 2007 | |
| dc.date.submitted | 2007-07-26 | |
| dc.identifier.citation | {1} D. Benson, Polynomial invariants of finite groups, London Mathematical Society Lecture Note
Series 190, Cambridge University Press,1993. {2} M.-J. Bertin, Anneaux d'invariants d'anneaux de polyn^{o}mes, en caract'{e}ristique p. C. R. Acad. Sci. Paris 277 (S'{e}rie A) (1973), 691-694. {3} D. Carlisle and P. Kropholler, Modular invariants of finite symplectic groups, Preprint. {4} D. Carlisle and P. Kropholler, Rational invariants of certain orthogonal and unitary groups, Bull. London Math. Soc. 24 (1992), 57-60. {5} L. Chiang; Y.-H. Hung, The invariants of Orthogonal group actions, Bull. Aust. Math. Soc. 1993, 48, 313-319. {6} H. Chu, Orthogonal Group Action on Rational Function Fields, Bull. Inst. Math. Acad. Sinica 1988, 16, 115-122. {7} H. Chu, Polynomial invariants of four-dimensional orthogonal groups, Communication in Algebra 29 (2001), 1153-1164. {8} H. Chu, Supplementary Note on 'Rational Invariants of Certain Orthogonal and Unitary Groups', Bull. London Math. Soc. 29 (1997), 37-42. {9} H. Chu and S.-Y. Jow, Polynomial invariants of finite unitary groups, Journal of Algebra 302 (2006), 686-719. {10} L. Dickson, A fundamental system of invariants of the general modular linear group with a solution of the form problem, Trans. A.M.S. 12 (1911), 75-98. {11} J.-H. Dung, On The Polynomial Invariants of Orthogonal Group Actions, Master Degree Thesis, Dept. of Math. National Taiwan Normal University, 2004. {12} E. Eisenbud, Commutative algebra with a view toward algebraic geometry, Graduate Texts in Mathematics 150, Springer-Verlag, 1994. {13} M. Hochster and J. A. Eagon, Cohen-Macaulay rings, invariant theory, and the generic perfection of determinantal loci, J. Math. 93 (1971), 1020-1058. {14} N. Jacobson, Basic Algebra, vol 1, W.H.Freeman and Com, 1984. {15} I. Kaplansky, Commutative rings, The university of Chicago Press, Chicago, 1974. {16} P. H. Kropholler, S. M. Rajaei and J. Segal, Invariant rings of orthogonal groups over $F_2$, Glasgow Math. J. 47 (2005), 7-54. {17} H. Nakajima, Relative invariants of finite groups, J. Algebra 79 (1982), 218-234. {18} S. M. Rajaei, Rational invariants of certain orthogonal groups over finite fields of characteristic two, Comm. Algebra 28 (2000), 2367-2393. {19} G.C. Shephard and J.A. Todd, finite unitary reflection groups, Canad. J. Math. 6 (1954), 274-304. {20} Z. Tang and Z-X Wan, A matrix approach to the rational invariants of certain classical groups over finite field of characteristic two, Finite Fields and Their Applications 12 (2006), 186-210. {21} K. Watanabe, Certain invariantssubrings are Gorenstein, I. Osaka J. Math. 11 (1974), 1-8. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/28545 | - |
| dc.description.abstract | 令 $Bbb F_q$ 是有 $q$ 個元素的 Galois 體, $Q_n$ 是 $Bbb F_q^n$ 上的非退化二次型且 $O_n(Bbb F_q)$ 是由 $Q_n$
定義的正交群。 令 $O_n(Bbb F_q)$ 線性地作用於多項式環 $Bbb F_q[x_1,x_2,dots,x_n]$ 上。 在本論文中, 我們將確切地 找出 $O_n(Bbb F_q)$ 的不變子環的生成元及其關係, 並且證明此不變子環是唯一分解環及完全交。 | zh_TW |
| dc.description.abstract | Let $Bbb F_q$ be the Galois field with $q$ elements, $Q_n$ a non-degenerated quadratic form on $Bbb F_q^n$, and
$O_n(Bbb F_q)$ the orthogonal group defined by $Q_n$. Let $O_n(Bbb F_q)$ act linearly on the polynomial ring $Bbb F_q[x_1,x_2,dots,x_n]$. In this paper, we will find explicit generators and relations for the ring of invariants of $O_n(Bbb F_q)$, and prove that it is a UFD and a complete intersection. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-13T00:11:38Z (GMT). No. of bitstreams: 1 ntu-96-R94221009-1.pdf: 475067 bytes, checksum: 47a0ee9605bd71ee6b8c1a0051b39494 (MD5) Previous issue date: 2007 | en |
| dc.description.tableofcontents | Acknowledgements..........................................i
Abstract in Chinese......................................ii Abstract................................................iii Contents.................................................iv 1 Introduction............................................1 2 The Notations and Elementary Properties.................5 3 The Statements of The Main Theorems....................20 4 Lemmas.................................................25 4.1 Two Key Lemmas.....................................25 4.2 Formulae on Polynomials Modulo Variables...........30 4.3 A Lemma on $R_n^{pm}$..............................38 4.4 Properties of Regular Sequence.....................43 5 Proposition $O_k$......................................48 6 The Proof of Theorem $O_{k+1}$.........................61 7 The Proof of Theorem $E_k^+$...........................71 8 The Proof of Theorem $E_k^-$...........................73 Reference................................................80 | |
| dc.language.iso | en | |
| dc.subject | 完全交 | zh_TW |
| dc.subject | 不變多項式 | zh_TW |
| dc.subject | 模正交群 | zh_TW |
| dc.subject | polynomial invariants | en |
| dc.subject | modular orthogonal group | en |
| dc.subject | complete intersection | en |
| dc.title | 有限正交群的不變多項式 | zh_TW |
| dc.title | Polynomial Invariants of Orthogonal Groups of Finite
Characteristics | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳永秋,陳榮凱,胡守仁,洪有情 | |
| dc.subject.keyword | 模正交群,不變多項式,完全交, | zh_TW |
| dc.subject.keyword | modular orthogonal group,polynomial invariants,complete intersection, | en |
| dc.relation.page | 82 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2007-07-30 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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