2015 Fiscal Year Final Research Report
Studies of Hirata separable extendions and related ring extensions
Project/Area Number |
23540049
|
Research Category |
Grant-in-Aid for Scientific Research (C)
|
Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Algebra
|
Research Institution | Okayama University |
Principal Investigator |
|
Project Period (FY) |
2011-04-28 – 2016-03-31
|
Keywords | 平田分離拡大 / 分離拡大 / ガロア拡大 / 平田分離多項式 / 分離多項式 / ガロア多項式 / 歪多項式環 |
Outline of Final Research Achievements |
In 1979, Yoichi Miyashita gave characterizations of a separable polynomial and a Hirata separable polynomial in skew polynomial rings. The research representative and Satoshi Yamanaka gave direct and elementary proofs of these theorems. Takasi Nagahara made a thorough investigation of separable polynomials and Galois polynomials of degree 2 in skew polynomial rings. The research representative and Satoshi Yamanaka tried to generalize Nagahara’s results for polynomials of degree 2 to general prime degree p case, and we had some interesting results.
|
Free Research Field |
代数学
|