Study on fundamental problems inside the undercurrent of Artinian rings

20世纪80年代初，Harada环的主要研究者引入了包含拟Frobenius环和Artin序列环的Harada环，并建立了这类环的结构理论，给出了以下结果：（1）Harada环包含一个框架拟Frobenius环，由该环构造Harada环。(2)A n-Artin序列环由拟Frobenius序列环构造.（3）拟Frobenius序列环表示为局部序列环上的斜矩阵环的因子环，在本研究项目中，主要研究者和研究者利用Harada环的理论对Artin环进行了综合研究，并从新的角度将其应用于拟Frobenius环和群代数的经典理论，做了几个口头报告：（1）Nakayama环的结构I，II，III ;代数闭域上Nakayama环的结构关于序群代数（日本数学学会，2005年3月）（2）关于费思猜想（美国凯洛大学数学研讨会，2005年3月）（3）拟Frobenius环和拟Frobenius代数的Nakayama自同构（Cailo大学代数研讨会，2005年3月）（4）序列代数和应用到代数闭域上的序列群代数（代数和共代数会议在开罗，2005年3月）根据这些基本结果，首席研究员与研究员巴巴一起写了一本书“阿廷环和相关主题”。这本书已基本完成，将于今年内出版。我们用这份手稿作为这份研究报告。

In the early 1980s, the head investigator introduced Harada rings which contain quasi-Frobenius rings and artinian serial rings, and established the structure theory on these rings by giving the following results :(1)A Harada ring contain a frame quasi-Frobenius.ring from which the ring is constructed.(2)A n artinian serial rings are constructed by quasi-Frobenius serial rings.(3)quasi-Frobenius serial rings are represented as factor rings of skew-matrix rings over local serial rings.Using the theory of Harada rings, in this research project, the head investigator together with investigators synthetically studied on artinian rings and applied to the classical theory on quasi Frobenius rings and group algebras from new point of view, and did several oral presentations :(1)Structure of Nakayama rings I,II,III ; On Kupisch series ; On structure of Nakayama rings over algebraically closed fields ; On setial group algebras (Japan Mathematics Society, March 2005)(2)On the Faith conjecture (American University of Cailo Mathematics Seminar, March 2005)(3)Nakayama automorphisms of quasi-Frobenius rings and quasi-Frobenius algebras (Cailo University Algebra Seminar, March 2005)(4)Serial algebras and applications to serial group algebras over algebraically closed fields (Algebra and Co-algebra Conference in Cairo, March 2005)Under these fundamental results, the head investigator together with investigator Baba are writing a book "Artinian Rings and Related Topics". This book is almost completed, and will be published within this year. We use this manuscript as this research report.