Some results on $(n,d)$-injective modules, $(n,d)$-flat modules and $n$-coherent rings

Zhu, Zhanmin. "Some results on $(n,d)$-injective modules, $(n,d)$-flat modules and $n$-coherent rings." Commentationes Mathematicae Universitatis Carolinae 56.4 (2015): 505-513. <http://eudml.org/doc/276261>.

@article{Zhu2015,
abstract = {Let $n,d$ be two non-negative integers. A left $R$-module $M$ is called $(n,d)$-injective, if $\{\rm Ext\}^\{d+1\}(N, M)=0$ for every $n$-presented left $R$-module $N$. A right $R$-module $V$ is called $(n,d)$-flat, if $\{\rm Tor\}_\{d+1\}(V, N)=0$ for every $n$-presented left $R$-module $N$. A left $R$-module $M$ is called weakly $n$-$FP$-injective, if $\{\rm Ext\}^n(N, M)=0$ for every $(n+1)$-presented left $R$-module $N$. A right $R$-module $V$ is called weakly $n$-flat, if $\{\rm Tor\}_n(V, N)=0$ for every $(n+1)$-presented left $R$-module $N$. In this paper, we give some characterizations and properties of $(n,d)$-injective modules and $(n,d)$-flat modules in the cases of $n\ge d+1$ or $n> d+1$. Using the concepts of weakly $n$-$FP$-injectivity and weakly $n$-flatness of modules, we give some new characterizations of left $n$-coherent rings.},
author = {Zhu, Zhanmin},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {$(n,d)$-injective modules; $(n,d)$-flat modules; $n$-coherent rings},
language = {eng},
number = {4},
pages = {505-513},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Some results on $(n,d)$-injective modules, $(n,d)$-flat modules and $n$-coherent rings},
url = {http://eudml.org/doc/276261},
volume = {56},
year = {2015},
}

TY - JOUR
AU - Zhu, Zhanmin
TI - Some results on $(n,d)$-injective modules, $(n,d)$-flat modules and $n$-coherent rings
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2015
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 56
IS - 4
SP - 505
EP - 513
AB - Let $n,d$ be two non-negative integers. A left $R$-module $M$ is called $(n,d)$-injective, if ${\rm Ext}^{d+1}(N, M)=0$ for every $n$-presented left $R$-module $N$. A right $R$-module $V$ is called $(n,d)$-flat, if ${\rm Tor}_{d+1}(V, N)=0$ for every $n$-presented left $R$-module $N$. A left $R$-module $M$ is called weakly $n$-$FP$-injective, if ${\rm Ext}^n(N, M)=0$ for every $(n+1)$-presented left $R$-module $N$. A right $R$-module $V$ is called weakly $n$-flat, if ${\rm Tor}_n(V, N)=0$ for every $(n+1)$-presented left $R$-module $N$. In this paper, we give some characterizations and properties of $(n,d)$-injective modules and $(n,d)$-flat modules in the cases of $n\ge d+1$ or $n> d+1$. Using the concepts of weakly $n$-$FP$-injectivity and weakly $n$-flatness of modules, we give some new characterizations of left $n$-coherent rings.
LA - eng
KW - $(n,d)$-injective modules; $(n,d)$-flat modules; $n$-coherent rings
UR - http://eudml.org/doc/276261
ER -