A study of integrated orders and its applications
| Project/Area Number |
21540056
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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 | Tokushima Bunri University |
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Principal Investigator |
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| Co-Investigator(Kenkyū-buntansha) |
植田 玲 島根大学 (70213345)
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| Project Period (FY) |
2009 – 2011
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| Project Status |
Completed (Fiscal Year 2011)
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| Budget Amount *help |
¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
Fiscal Year 2011: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2010: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2009: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Keywords | 環論 / Skew polynomial / Prime ideal / Localizing system / Prime factor ring / Dedekind domain / Crossed product / Ore extension / Prufer ring / Total valuation / Derivation / Prime ring / Partial skew polynomial / Fully bounded / GCD order / Gauss extension / Graded extension / Non-commutative valuation ring / Residue skew field / Skew Laurent polynomial |
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| Research Abstract |
We have mainly studied the algebraic structure of the following five different types of rings.
(1) Let R be a partial skew polynomial ring over a semi-simple Artinain ring. We proved there are three different central idempotent in R. Furthermore we determined the structure of prime radical of R and proved that any prime ideals of R is either a maximal ideal and principal or idempotent.
(2) Let R be an Ore extension over a non-commutative valuation ring. We proved that R is always a generalized Bezout. Further we obtained that a necessary and sufficient conditions for R to be fully bounded.
(3) We classified the prime ideals of crossed product algebras over non-commutative valuation rings.
(4) We classified the localizing system of Prufer rings.
(5) We classified the prime ideals in skew polynomial rings over commutative Dedekind domain and determined the structure of the prime factor rings.
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Report
(4 results)
Research Products
(18 results)
