Research of quasi-Frobenius rings and representation theory

拟弗罗贝尼乌斯环及表示论研究

• 批准号: 12640027
• 负责人: YOSHIMURA Hiroshi
• 金额: $ 0.83万
• 依托单位: Yamaguchi University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2000
• 资助国家: 日本
• 起止时间: 2000 至 2001
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-12640027/
• 关键词: Ring theory; Quasi-Frobenius rings; Extending modules; Self-duality of rings; Von-Neumann regular rings; 多元環

This research in concerned with quasi-Frobenius rings and their representation theory. Allotting a portion of the project to each investigator, I studied the structures and representations of quasi-Frobenius rings and related rings. Consequently, we obtained the following results.1. We constructed an algorithm for deciding whether a given factor algebra of a polynomial ring over a field is quasi-Frobenius and implemented the algorithm to computers. By this method, we completely determined the isomorphism classes of commutative quasi-Frobenius algebras with radical cube zero.2. We determined the condition for extending modules to be closed under finite direct sums and investigated self-duality of Auslander rings of local serial rings.3. We studied the "Direct Finite" property of modules of von-Neumann regular rings with weak comparability axiom.4. We also obtained other related results to this research.

本研究涉及拟frobenius环及其表示理论。我将项目的一部分分配给每个研究者，研究了拟frobenius环和相关环的结构和表示。因此，我们得到了以下结果。构造了判定域上多项式环的给定因子代数是否为拟frobenius的算法，并在计算机上实现了该算法。利用该方法，我们完全确定了具有根立方0的交换拟frobenius代数的同构类。我们确定了扩展模在有限直接和下闭的条件，研究了局部序列环的Auslander环的自对偶性。利用弱可比性公理研究了von-Neumann正则环模的“直接有限”性质。我们还获得了与本研究相关的其他结果。

项目成果

H.Yoshimura, and I.Kikumasa: "Some type of commutative artin algebras"Kokyuroku, RIMS. 1222. 24-33 (2001)

H.Yoshimura 和 I.Kikumasa：“某种类型的交换 artin 代数”Kokyuroku，RIMS。

Y.Baba, and H.Miki: "Symmetry of almost hereditary rings"Math J. Okayama Univ.,. (to appear).

Y.Baba 和 H.Miki：“几乎遗传环的对称性”Math J. 冈山大学，。

Isao Kiuchi: "On the mean value formula for the non-symmetric form of approximate functional equation of ζ^2(s) in the critical strip"Publ. Math. Debrecen. 58/1-2. 109-119 (2001)

Isao Kiuchi：“关于临界带中 ze^2(s) 的非对称形式的平均值公式”Publ. 58/1-2 (2001)。

Yoshitomo Baba: "On self-duality of Auslander rings of local serial rings"Comm. in Algebra. (予定). (2002)

Yoshitomo Baba：《代数中的 Auslander 环的自对偶性》（计划）。

K.Kuriyama(その他2): "Sesquilinear forms induced by a positive linear form on *-algebra and application to geneeralized uncertainty relations"The 9th International Conf.on Finite or Infinie Dim.Coomplex Analysis and Appl. 86-87 (2001)

K. Kuriyama（其他 2）：“*-代数上的正线性形式引发的倍数线性形式及其在广义不确定性关系中的应用”第 9 届国际有限或无限维会议。Cocomplex Analysis and Appl. 86-87 (2001)