| Project/Area Number |
15K04826
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Tokyo Metropolitan University |
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Principal Investigator |
Kuroda Shigeru 首都大学東京, 理学研究科, 教授 (70453032)
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| Research Collaborator |
Kojima Hideo 新潟大学, 大学院自然科学研究科, 教授 (90332824)
Tanimoto Ryuji 静岡大学, 教育学部, 准教授 (20547062)
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| Project Period (FY) |
2015-04-01 – 2019-03-31
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| Project Status |
Completed (Fiscal Year 2018)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2017: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
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| Keywords | 多項式環 / 自己同型写像 / 安定余順自己同型 / 加法群作用 / ヒルベルトの第14問題 / 余順自己同型 / レンチュラー・宮西の定理 / 多項式自己同型 / Hilbertの第14問題 / 順部分群 / 標数位数自己同型 |
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| Outline of Final Research Achievements |
A polynomial is an indispensable concept in mathematics, and the ring formed by them is a basic object in modern algebra. However, there remain various difficult open problems concerning polynomial rings, which have been studied worldwide. In the study of such problems, automorphisms of a polynomial ring and the ring formed by them play important roles. In this research, we investigated subgroups of the automorphism group of a polynomial ring and related objects, and obtained various new information about them. We also succeeded in constructing a new counterexample to Hilbert's fourteenth problem by using the knowledge of polynomial automorphisms.
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| Academic Significance and Societal Importance of the Research Achievements |
ヒルベルトの基底定理をはじめ，多項式環に関する基本的な結果は，現代代数学において重要な役割を果たしている．多項式環の基本的な性質については未だ不明な点が多く，それらを解明することは，将来的に代数学の発展に多大な貢献をするはずである．多項式環の自己同型や自己同型群は，多項式環を理解するうえで欠かせないものであり，本研究で得られた成果は，今後の多項式環研究で重要な意味を持つと考えられる．
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