2012 Fiscal Year Final Research Report
Modular invariant theory of finite cyclic groups
| Project/Area Number |
22740009
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| Research Category |
Grant-in-Aid for Young Scientists (B)
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| Allocation Type | Single-year Grants |
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| Research Field |
Algebra
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| Research Institution | Shizuoka University |
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Principal Investigator |
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| Project Period (FY) |
2010 – 2012
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| Keywords | モジュラー不変式論 / 計算不変式論 / グレブナー基底 / 有限巡回群 |
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| Research Abstract |
We studied computational algebraic methods in modular invarianttheory of finite cyclic groups, and we constructed the following algorithms. We constructed, via defining a Reynolds-like operator, an algorithm for computing generators of modular invariant rings of cyclic groups of prime order. Furthermore, given a polynomial ring over a field of positive characteristic pand an automorphism of order pof the polynomial ring, we constructed the image membership algorithm for the twisted derivation associated with the automorphism
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