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

Czechoslovak Mathematical Journal (2014)

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

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topLi, 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 -

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