Synthetic Study of Prufer Orders and Semi-hereditary Orders

普鲁弗令和半世袭令的综合研究

• 批准号: 13640030
• 负责人: MARUBAYASHI Hidetoshi
• 金额: $ 1.79万
• 依托单位: Naruto University of Education
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2001
• 资助国家: 日本
• 起止时间: 2001 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640030/
• 关键词: Valuation ring; Total valuation; Invariant valuation; Crossed product algebra; Prime ideal; Primary ideal; Ore extension; Martindal quotient ring; Primaty ideal; Ore extensions; Martindale quotient rings; Crossed product; Tamely ramified; val

For 2001-2004, we have studied the following four projects which are all concerned with non-commutative valuation rings :1.We gave a necessary and sufficient conditions for a Dubrovin valuation ring to be fully bounded by using the concept of the prime segments.2.Martindale quotient rings of Dubrovin valuation rings are determined in terms of the localizations.3.We have studied non-commutative valuation rings of Ore extensions and found out several important non-commutative valuation rings of Ore extensions.4.Let G be a totally ordered group and let V be a total valuation ring. We have studied non-commutative valuation rings of the crossed product algebra V G by the graded theoretical methods.

2001-2004年，我们研究了以下四个与非交换赋值环有关的课题：1.利用素段的概念给出了Dubrovin赋值环是完全有界的充要条件; 2.利用局部化确定了Dubrovin赋值环的Martindale商环; 3.研究了Ore扩张的非交换赋值环，并找到了Ore扩张的几个重要的非交换赋值环; 4.设G是全序群，V是全赋值环.利用分次理论方法研究了交叉积代数VG的非交换赋值环。

项目成果

丸林英俊: "Non-commutative valuation rings of the quotient Artinian ring of a skew polynomial rings"Algebras and Representation Theory. (to appear).

Hidetoshi Marubayashi：“斜多项式环的商 Artinian 环的非交换估价环”代数和表示论（即将出现）。

丸林英俊: "On Semi-hereditary over commutative valuation rings"Journal of Algebras. (to appear).

Hidetoshi Marubayashi：“关于交换估价环的半遗传性”代数杂志（待发表）。

On R-Ideals of a Dubrovin Valuation Ring R

• DOI: 10.1081/agb-120027865
• 发表时间: 2004-03
• 期刊: Communications in Algebra
• 影响因子: 0.7
• 作者: S. Irawati;H. Marubayashi;A. Ueda

Total valuation rings of Ore extensions

矿石延伸的总估价环

• 发表时间: 2003
• 期刊: Results in Math. 43
• 作者: 丸林英俊;丸林英俊;丸林英俊;丸林英俊
• 通讯作者: 丸林英俊

Prime segments for cones and rings

圆锥体和环的主要分段

• 发表时间: 2003
• 期刊: Fields Institute Communications, Valuation Theory and its Applications 2
• 作者: H.Brungs;H.Marubayashi;E.Osmanagic
• 通讯作者: E.Osmanagic