2011 Fiscal Year Final Research Report
A unified theory of Grobner bases and an application to syzygies of modules
| Project/Area Number |
21540048
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Algebra
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| Research Institution | Toho University |
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Principal Investigator |
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| Project Period (FY) |
2009 – 2011
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| Keywords | グレブナー基底 / シチジー / 書き換えシステム / 順序半群 / イデアル / 加群 / 完備化 |
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| Research Abstract |
We develop a unified theory of Grobner bases, and apply it to various calculations concerning algebras, ideals and modules. We construct a theory on an algebra F based on a well-ordered semigroup and on a projective F-module FX, and we prove the critical pair theorem. We obtain a main result that the cycles made from critical pairs in FH form a generating system of syzygies, if H is a Grobner basis on FX.
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