( n , d ) -injective covers, n -coherent rings, and ( n , d ) -rings

Weiqing Li; Baiyu Ouyang

Czechoslovak Mathematical Journal (2014)

  • Volume: 64, Issue: 2, page 289-304
  • ISSN: 0011-4642

Abstract

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It is known that a ring R is left Noetherian if and only if every left R -module has an injective (pre)cover. We show that ( 1 ) if R is a right n -coherent ring, then every right R -module has an ( n , d ) -injective (pre)cover; ( 2 ) if R is a ring such that every ( n , 0 ) -injective right R -module is n -pure extending, and if every right R -module has an ( n , 0 ) -injective cover, then R is right n -coherent. As applications of these results, we give some characterizations of ( n , d ) -rings, von Neumann regular rings and semisimple rings.

How to cite

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Li, Weiqing, and Ouyang, Baiyu. "$(n,d)$-injective covers, $n$-coherent rings, and $(n,d)$-rings." Czechoslovak Mathematical Journal 64.2 (2014): 289-304. <http://eudml.org/doc/261991>.

@article{Li2014,
abstract = {It is known that a ring $R$ is left Noetherian if and only if every left $R$-module has an injective (pre)cover. We show that $(1)$ if $R$ is a right $n$-coherent ring, then every right $R$-module has an $(n,d)$-injective (pre)cover; $(2)$ if $R$ is a ring such that every $(n,0)$-injective right $R$-module is $n$-pure extending, and if every right $R$-module has an $(n,0)$-injective cover, then $R$ is right $n$-coherent. As applications of these results, we give some characterizations of $(n,d)$-rings, von Neumann regular rings and semisimple rings.},
author = {Li, Weiqing, Ouyang, Baiyu},
journal = {Czechoslovak Mathematical Journal},
keywords = {cover; envelope; $n$-coherent ring; $(n,d)$-injective; $(n,d)$-ring; injective covers; injective precovers; injective envelopes; coherent rings; injective modules; -rings},
language = {eng},
number = {2},
pages = {289-304},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {$(n,d)$-injective covers, $n$-coherent rings, and $(n,d)$-rings},
url = {http://eudml.org/doc/261991},
volume = {64},
year = {2014},
}

TY - JOUR
AU - Li, Weiqing
AU - Ouyang, Baiyu
TI - $(n,d)$-injective covers, $n$-coherent rings, and $(n,d)$-rings
JO - Czechoslovak Mathematical Journal
PY - 2014
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 64
IS - 2
SP - 289
EP - 304
AB - It is known that a ring $R$ is left Noetherian if and only if every left $R$-module has an injective (pre)cover. We show that $(1)$ if $R$ is a right $n$-coherent ring, then every right $R$-module has an $(n,d)$-injective (pre)cover; $(2)$ if $R$ is a ring such that every $(n,0)$-injective right $R$-module is $n$-pure extending, and if every right $R$-module has an $(n,0)$-injective cover, then $R$ is right $n$-coherent. As applications of these results, we give some characterizations of $(n,d)$-rings, von Neumann regular rings and semisimple rings.
LA - eng
KW - cover; envelope; $n$-coherent ring; $(n,d)$-injective; $(n,d)$-ring; injective covers; injective precovers; injective envelopes; coherent rings; injective modules; -rings
UR - http://eudml.org/doc/261991
ER -

References

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