A study of integrated orders and its applications

综合订单及其应用研究

• 批准号: 21540056
• 负责人: MARUBAYASHI Hidetoshi
• 金额: $ 1.58万
• 依托单位: Tokushima Bunri University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2009
• 资助国家: 日本
• 起止时间: 2009 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-21540056/
• 关键词: 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 extensio

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.

我们主要研究了以下五种不同类型的环的代数结构。(1)设R是半单Artinain环上的部分斜多项式环。证明了R中存在三个不同的中心幂等元。进一步确定了R的素根的结构，证明了R的任何素理想都是极大理想和主理想或幂等元。(2)设R是非交换赋值环上的Ore扩张。我们证明了R总是广义Bezout。进一步得到了R是完全有界的一个充要条件。(3)对非交换赋值环上交叉积代数的素理想进行了分类。(4)对Prufer环的局部化系统进行了分类。(5)对交换Dedekind整环上的斜多项式环的素理想进行了分类，确定了素因子环的结构。

项目成果

Partial skew polynomial over semisimple Artinain rings

半单 Artinain 环上的部分偏斜多项式

• 发表时间: 2010
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: H.Marubayashi;M.Ferrero
• 通讯作者: M.Ferrero

The group of divisors of an Ore extension over a Noetherian integrally closed domain

诺特积分闭域上 Ore 扩展的约数群

• 发表时间: 2010
• 期刊: The Aligarh Bulletin of Math
• 作者: W. Cortes;M. Ferrero;H. Marubayashi and Y. Hirano;H. Marubayashi and Y. Wang
• 通讯作者: H. Marubayashi and Y. Wang

Prime Divisors and Noncommutative Valuation Rings

素数和非交换估值环

• 发表时间: 2012
• 作者: H.Marubayashi;F.Van Oystaeyen
• 通讯作者: F.Van Oystaeyen

Residue skew fields of Gauss extensions in K(X ; σ)

K(X ; σ) 中高斯扩展的剩余偏斜场

• 发表时间: 2010
• 期刊: JP Journal of Algebra, Number Theory and Applications 16
• 作者: H.Marubayashi;G.Xie;Y.Wang
• 通讯作者: Y.Wang

Prime Divisors and Non-commutative Valuation Rings

质因数和非交换估值环

• 发表时间: 2012
• 作者: H.Marubayashi;Y.Wang;H.Marubayashi;H. Marubayashi;H. Marubayashi and F. Van Oystaeyen
• 通讯作者: H. Marubayashi and F. Van Oystaeyen