SP-代数和C-平坦模

发布时间：2018-02-02 13:54

本文关键词： (S)G-内射模不可约态射单模 IG-内射模 Auslander-Reiten箭图 SP-代数 C-内射模 C-平坦模　出处：《南京师范大学》2015年硕士论文　论文类型：学位论文

【摘要】：本文中主要研究了如下几个方面的内容：第一部分,在G-内射模和SG-内射模的定义和性质基础上,运用不可约态射的性质,引入IG-内射模的概念.主要研究了IG-内射模的几个等价刻划,并且证明了若单模都是SG-内射模,则该单模是内射模或者有一个从内射模到该单模的不可约态射.进一步我们证明了环R上的模是单模与内射模的直和.第二部分,我们在IG-内射模和Auslander-Reiten箭图的基础上,研究若模modR=S(R)(?)P(R),则该模的代数是什么形式.我们给出了其具体的代数形式,并进行了一一论证.第三部分,在C-内射模的基础上,我们引入了C-平坦模的概念,给出了C-平坦模的一些基本性质,研究了C-平坦模和C-内射模的关系,最后给出了构造C-平坦模的基本方法.
[Abstract]:This paper mainly studies the following aspects: the first part, based on the definition and properties of G- injective modules and SG- injective modules, using the properties of irreducible morphisms, introducing the concept of IG- injective modules. Mainly studied several equivalent IG- injective modules in the characterization, and it is proved that if SG- is single injective modules, the single mode is injective or one from injective modules to the single irreducible morphisms. We further prove that the ring on the R mode is straight and single-mode and injective modules. In the second part, we based on IG- injective modules and Auslander-Reiten quivers, if the study mode modR=S (R) (?) P (R), then the model is what algebraic form. We give the algebraic form, and one by one argument. The third part, based on C- injective modules, we introduce the concept of C- flat modules, gives some basic properties of C- flat modules study. The relationship between the C- flat mode and the C- injective module is given. Finally, the basic method of constructing the C- flat mode is given.

【学位授予单位】：南京师范大学
【学位级别】：硕士
【学位授予年份】：2015
【分类号】：O153.3

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