Research of automatic structure which appear in algebras

代数中出现的自动结构的研究

• 批准号: 10640030
• 负责人: KOBAYASHI Shigeru
• 金额: $ 1.66万
• 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: 1998
• 资助国家: 日本
• 起止时间: 1998 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10640030/
• 关键词: Automaton; Local cohomology; Groebner basis; Torsion theory; Inverse semigroups; Valuation ring; Weyl algebras; ワイル代数; 局所コホモロジー群; モデル理論; 述語論理; 連分数展開; stability theory

I researched automatic structure which appears in algebras.(1) Automatic structure of semi-group theory.There is a rational operation in semi-groups and generation D = J is filled in the equivalent relation of Green. It was able to divide into three types and we could obtain the structure.(2) Automatic structure of ring theory.Local cohomology of Weyl algebra can be calculated by using Groebner basis and Torsion theory. We obtained the algorithm to calculate extension of non-commutative valuation ring under some conditions. And another I researched automatic structure of number theory and logic.

我研究了代数中的自动结构。(1)半群理论的自动结构。在半群中存在一个有理运算，代D = J填充在Green的等价关系中。它可以分为三种类型，我们可以得到结构。(2)环理论的自动结构。利用Groebner基和扭转理论可以计算Weyl代数的局部上同调。给出了在一定条件下计算非交换值环可拓的算法。另一个是研究数论和逻辑的自动结构。

项目成果

小林滋: "The submanifolds of self-dual codes in a Grassmann manifolds" 数理解析研究所講究録. 1063. 163-169 (1998)

Shigeru Kobayashi：“格拉斯曼流形中自对偶码的子流形”数学分析研究所的 Kokyuroku 1063. 163-169 (1998)。

Shigeru Kobayashi: "On rings whose faithful modules, which is generated at most two elements, are generator"Math. Japonica. Vol. 52. 263-265 (2000)

Shigeru Kobayashi：“在环上，其忠实模块（最多生成两个元素）是生成器”数学。

小林 滋: "L-classes of inverse semigroups"Applied Mathematics E-notes. 1. 111-117 (2001)

小林茂：“逆半群的 L 类”应用数学电子笔记 1. 111-117 (2001)。

小林 滋: "Total valuation rings of K(X,σ) containing K"Communication of algebras. 14

小林茂：“包含 K 的 K(X,σ) 的总估价环”代数通讯 14。

S.Kobayashi: "On rings whose faithful modules, which is generated at most two elements, are generator"Mathematica Japonica. 52-2. 263-265 (2000)

S.Kobayashi：“在环上，其忠实模（最多生成两个元素）是生成器”Mathematica Japonica。