| 朱占敏.强n-凝聚环[J].数学年刊A辑,2017,38(3):313~326 |
| 强n-凝聚环 |
| Strongly n-Coherent Rings |
| Received:July 28, 2014 Revised:June 05, 2016 |
| DOI：10.16205/j.cnki.cama.2017.0027 |
| 中文关键词: Strongly $n$-injective module, Strongly $n$-flat module, Strongly $n$-coherent ring, $n$-Semihereditary ring |
| 英文关键词:Strongly $n$-injective module, Strongly $n$-flat module, Strongly $n$-coherent ring, $n$-Semihereditary ring |
| 基金项目: |
|
| Hits: 849 |
| Download times: 718 |
| 中文摘要: |
| 设$R$是一个环, $n$是一个正整数. 右$R${-}模$M$称为强$n${-}内射的,
如果从任一自由右$R${-}模$F$的任一$n${-}生成子模到$M$的同态都可扩张为$F$到$M$的同态;
右$R${-}模$V$称为强$n${-}平坦的, 如果对于任一自由右$R${-}模$F$的任一$n${-}生成子模$T$,
自然映射$V\otimes T\rightarrow V\otimes F$是单的; 环$R$称为左强$n${-}凝聚的,
如果自由左$R${-}模的$n${-}生成子模是有限表现的; 环$R$称为左$n${-}半遗传的,
如果$R$的每个$n${-}生成左理想是投射的.本文研究了强$n${-}内射模, 强$n${-}平坦摸及左强$n${-}凝聚环.
通过模的强$n${-}内射性和强$n${-}平坦性概念, 作者还给出了强$n${-}凝聚环和$n${-}半遗传环的一些刻画. |
| 英文摘要: |
| Let $R$ be a ring and $n$ a fixed positive integer.
A right $R$-module $M$ is called strongly $n$-injective if every $R$-homomorphism
from an $n$-generated submodule of a free right $R$-module $F$ to $M$ extends to
a homomorphism of $F$ to $M$; a right $R$-module $V$ is said to be strongly $n$-flat,
if for every $n$-generated submodule $T$ of a free right $R$-module $F$, the canonical
map $V\otimes T\rightarrow V\otimes F$ is monic; a ring $R$ is called left strongly
$n$-coherent if every $n$-generated submodule of a free left $R$-module is finitely presented;
ring $R$ is said to be left $n$-semihereditary if every $n$-generated left ideal of $R$ is
projective. The author studies strongly $n$-injective modules, strongly $n$-flat modules and left strongly
$n$-coherent rings. Using the concepts of strongly $n$-injectivity and strongly $n$-flatness of modules,
the author also presents some characterizations of strongly $n$-coherent rings and $n$-semihereditary rings. |
| View Full Text View/Add Comment Download reader |
| Close |
|
|
|
|
|
