2013 Fiscal Year Final Research Report
Research on arithmetic of algebraic number fields by practical use of generic polynomials
| Project/Area Number |
23540029
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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 University of Science |
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Principal Investigator |
KOMATSU Toru 東京理科大学, 理工学部, 講師 (10403974)
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| Project Period (FY) |
2011 – 2013
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| Keywords | アルゴリズム / 代数学 |
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| Research Abstract |
In this research we give a sufficient condition on the Galois type for the non-existence of a number field which has a certain inertia property. The number of Galois types up to degree nine is 121, the sufficient condition holds for 58 types, not for 63 types. For the latter 63 types we concretely demonstrate the existence of such number fields by using tables and computer softwares.
In addition we generalize a result which is one of bases for this research. We show the existences of ideals with a certain condition in imaginary quadratic fields.
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