Homological structure and representation of Noetherian algebras

诺特代数的同调结构和表示

• 批准号: 11640020
• 负责人: NISHIDA Kenji
• 金额: $ 1.98万
• 依托单位: Shinshu University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1999
• 资助国家: 日本
• 起止时间: 1999 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-11640020/
• 关键词: Noetherian algebra; Gorenstein Algebra; Gorenstein dimension; dualizing module; order; アルティン多元環; ネータ環; バス予想; 有限入射次元; 完全加群

We consider a theory of non-commutative Noetherian algebras as commutative ring theory. Mainly, we consider an algebra which is finitely generated as a module over a commutative Noetherian ring. We define a Gorenstein algebra by the Cousin complex and give a characterization of a Gorenstein algebra by the Bass number. Indeed, the fact concerning Bass numbers holds completely similar to that of commutative rings. We extend the results due to R. Y. Sharp to our algebras, namely, under some assumption, we give a category equivalence between the category of finite modules of finite injective dimension and that of finite modules of finite protective dimension. We give a criterion that a module over an order or artin algebra is a dualizing modulen and apply it to a Cohen-Macaulay isolated singularities. We study a global dimension of a tiled oreder. Especially, we give a theory to deal with a tiled order having a large global dimension.

我们考虑了非交换诺埃尔代数的交换环理论。主要考虑一个有限生成的代数，它是交换诺瑟环上的一个模。我们用表兄复合体定义了Gorenstein代数，并用Bass数给出了Gorenstein代数的一个表征。事实上，关于Bass数的事实与交换环的事实完全相似。我们将R. Y. Sharp的结果推广到代数上，即在一定的假设下，给出了有限内射维的有限模的范畴与有限保护维的有限模的范畴之间的范畴等价。给出了一阶代数上的模是对偶模的判据，并将其应用于Cohen-Macaulay孤立奇点。我们研究平铺订单的全局维度。特别是，我们给出了一个理论来处理具有大全局维度的平铺订单。

项目成果

Yasuo Iwanaga : "Note on Waka matsu's generalized tilting modules"Journal of the Faculty of Education, Shinshu Univ.. 99. 155-166 (2000)

Yasuo Iwanaga：“关于和歌松广义倾斜模块的注释”信州大学教育学院学报.. 99. 155-166 (2000)

Akihide Hanaki,Izumi Miyamoto: "Classification of primitive association schemes with small vertices"Kyashu J.Math. 54・7. 81-86 (2000)

Akihide Hanaki，Izumi Miyamoto：“具有小顶点的原始关联方案的分类”Kyashu J.Math 54・7（2000）。

Y.Ninomiya: "Nilpotency indices of the radical of tinitep-solvable group algbras, I"J.Anstral.Math.Soc.. 71. 117-133 (2001)

Y.Ninomiya：“tinitep 可解群代数的自由基的幂指数，I”J.Anstral.Math.Soc.. 71. 117-133 (2001)

Yasusi Ninomiya : "Nilpotency indices of the radicals of finite β-solvabe group algebras, I"J.Austral.Math, Soc.,SerA, . (to appear).

Yasusi Ninomiya：“有限 β-可解群代数的根的幂幂指数，I”J.Austral.Math，Soc.，SerA，（即将出现）。

Kenji Nishida, Shiro Goto: "Catenarity in module-finite algebras"Proc. Amer. Math. Soc.. 127. 3495-3502 (1999)

Kenji Nishida、Shiro Goto：“模有限代数中的悬链线”Proc。