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

Title:

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

Creator:

Li, Weiqing and Ouyang, Baiyu

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:0a306832-519a-4182-b59b-6f17073ce2dd
uuid:0a306832-519a-4182-b59b-6f17073ce2dd

Subject:

cover, envelope, $n$-coherent ring, $(n,d)$-injective, and $(n,d)$-ring

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

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.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

289-304

Source:

Czechoslovak Mathematical Journal | 2014 Volume:64 | Number:2

Harvested from:

CDK

Metadata only:

false