权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Study on Artinian rings with priority given to Quasi-Frobenius rings

以准弗罗贝尼乌斯环为主的阿天尼环研究

基本信息

批准号：
13640028
负责人：
OSHIRO Kiyoichi
金额：
$ 2.24万
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：
2001
资助国家：
日本
起止时间：
2001 至 2002
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-13640028/
关键词：
OF-ring Nakayama ring Harada ring Skew-Matrix ring extending module lifting module generalized relative injectivity generalized relative projectivity Artinian ring Quasi-Frobenius ring sjkew-matrix ring Nakayama-permutation Nakayam

项目摘要

(1) head investigator Oshiro has been extensively studied on Quasi-Frobeniu ring and Nakayama ring as applications of Harada rings (which was introduced by Oshiro). In research [1], Oshiro gave a survey on Harada ring and applications, most of which is due to Oshiro(2) In [2],[3], we studied the open problem when direct sum of extending modules are extending modules. We readied to a situation that this problem should be studied by considering two types. In this paper, we completely solved on one type, by introducing generalized relative injectivity. Recently, this generalized relative injectivity is called "objectivity" (Oshiro injectivity)(3)Dr Kuratomi is a student of the headinvestigator. In [6], he studied dual result of [3] and gave a very nice result.(4) Oshiro [1],[2],[3], Baba [4], Koike [5], Kuratomi [6] are important papers for this research project. In particular, in [5], Koike discovered an exsample of a Quasi-Frobenius ring without Nakayama automorphism. This result is a very important and , in some sense, this paper completes the headinvestigator's many years study on Artinian rings.

(1)作为Harada环应用，Oshiro对Quasi-Frobeniu环和Nakayama环进行了广泛的研究。在[1]中，Oshiro对Harada环及其应用作了综述，其中大部分是由于Oshiro的研究（2）在[2]、[3]中，我们研究了扩张模的直和是扩张模的公开问题。我们准备了一个情况，这个问题应该考虑两种类型的研究。本文通过引入广义相对内射性，完全解决了其中一类问题。最近，这种广义的相对内射性被称为“客观性”（Oshiro内射性）（3）仓富博士是首席研究员的学生。在[6]中，他研究了[3]的对偶结果，并给出了一个很好的结果. (4)Oshiro [1]，[2]，[3]，Baba [4]，Koike [5]，Kuratomi [6]是本研究项目的重要论文。特别地，在[5]中，Koike发现了一个没有Nakayama自同构的拟Frobenius环的exsample。这个结果是一个非常重要的结果，在某种意义上，它完成了首席研究员多年来对Artin环的研究。