2005 Fiscal Year Final Research Report Summary
Study on fundamental problems inside the undercurrent of Artinian rings
| Project/Area Number |
15540034
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Algebra
|
|---|
| Research Institution | Yamaguchi University |
|---|
Principal Investigator |
OSHIRO Kiyoichi Yamaguchi University, Faculty of Science, Professor, 理学部, 教授 (90034727)
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
KUTAMI Mamoru Yamaguchi University, Faculty of Seience, Professor, 理学部, 教授 (80034734)
YOSHIMURA Hiroshi Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (00182824)
KIKUMASA Isao Yamaguchi University, Faculty of Science, Associate Professor, 理学部, 助教授 (70234200)
IIYORI Nobuo Yamaguchi University, Faculty of Education, Associate Professor, 教育学部, 助教授 (00241779)
BABA Yoshitomo Osaka Education University, Faculty of Education, Associate Professor, 教育学部, 助教授 (10201724)
|
|---|
| Project Period (FY) |
2003 – 2005
|
| Keywords | QF-ring / Nakayama ring / Harada ring / skew-matrix ring / continuous ring / Morita duality / lifting module / extending module |
|---|
| Research Abstract |
In the early 1980s, the head investigator introduced Harada rings which contain quasi-Frobenius rings and artinian serial rings, and established the structure theory on these rings by giving the following results :
(1)A Harada ring contain a frame quasi-Frobenius.ring from which the ring is constructed.
(2)A n artinian serial rings are constructed by quasi-Frobenius serial rings.
(3)quasi-Frobenius serial rings are represented as factor rings of skew-matrix rings over local serial rings.
Using the theory of Harada rings, in this research project, the head investigator together with investigators synthetically studied on artinian rings and applied to the classical theory on quasi Frobenius rings and group algebras from new point of view, and did several oral presentations :
(1)Structure of Nakayama rings I,II,III ; On Kupisch series ; On structure of Nakayama rings over algebraically closed fields ; On setial group algebras (Japan Mathematics Society, March 2005)
(2)On the Faith conjecture (American University of Cailo Mathematics Seminar, March 2005)
(3)Nakayama automorphisms of quasi-Frobenius rings and quasi-Frobenius algebras (Cailo University Algebra Seminar, March 2005)
(4)Serial algebras and applications to serial group algebras over algebraically closed fields (Algebra and Co-algebra Conference in Cairo, March 2005)
Under these fundamental results, the head investigator together with investigator Baba are writing a book "Artinian Rings and Related Topics". This book is almost completed, and will be published within this year. We use this manuscript as this research report.
|
