2000 Fiscal Year Final Research Report Summary
Research on clarifying algebraic structure of rings using each representation theory of algebras, group rings and Lie rings.
Project/Area Number 
11640019

Research Category 
GrantinAid for Scientific Research (C)

Allocation Type  Singleyear Grants 
Section  一般 
Research Field 
Algebra

Research Institution  Yamanashi University 
Principal Investigator 
SATO Masahisa Faculty of Engineering, Yamanashi University Professor, 工学部, 教授 (30143952)

CoInvestigator(Kenkyūbuntansha) 
IWANAGA Yasuo Shinshu University, Faculty of Education, Professor, 教育学部, 教授 (80015825)
MIYAMOTO Izumi Faculty of Engineering, Yamanashi University Professor, 工学部, 教授 (60126654)
KURIHARA Mitsunobu Faculty of Engineering, Yamanashi University Professor, 工学部, 教授 (50027372)

Project Period (FY) 
1999 – 2000

Keywords  Ring / Representation / Algebra / Lie Algebra / Noeterian Ring / Group ring / Association Scheme 
Research Abstract 
[1999] In Duality theory Sato studied the principle of Duality which exists in Commutative noetherian ring and analyzed it in the view point of general noncommutative ring theory. By using noncommutative ring theory method, he succeeded to find the essential principle that Duality exists. which was difficult to find in the case of commutative ring since several facts were mixed to be held one fact. Also he showed theses facts hold also in the case of noncommutative rings under some conditions. Miyamoto studied about Association scheme which is notified recently and he decided these which has elements up to 22. Iwanaga generalized Wakamatsu theorem, which is famous theorem in the field of the representation theory of algebras, with respect to Tilting algebra. Kurihara advised on researched through discussion about the above studies. [2000] Sato studied global dimension of typical case of quasihereditary rings which had been introduced from the representation theory of Lie algebras. For the ring you make the endomorphism ring of direct sum of all modules of the ring modulo the power of its Jacobson radical, then this ring becomes quasihereditary. He completely find the structure of minimal projective resolution of simple modules of this endomorphism ring and using this properties, he created the way of construction of resolution of these modules. Also he proved the global dimension does not exceed the number of simple modules. Miyamoto found the construction of groups which includes normalizer of permutation groups by using association scheme noticed as generalization of group rings. Iwanaga continued the study of the generalization of Wakamatsu theorem. Kurahara gave advises in the stand point of view of analysis through discussions.

Research Products
(12 results)