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On rings with envelopes and covers regarding to $C 3$ $C 3$ , $D 3$ $D 3$ and flat modules

Le Van Thuyet

Department of Mathematics, College of Education, Hue University, 34 Le Loi, Hue City, Vietnam

E-mail Address: lvthuyet@hueuni.edu.vn

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Phan Dan

Hong Bang International University, 215 Dien Bien Phu Street, Binh Thanh, Ho Chi Minh City, Vietnam

E-mail Address: gmphandan@gmail.com

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, and

Truong Cong Quynh

Department of Mathematics, The University of Danang — University of Science and Education, 459 Ton Duc Thang, Danang City, Vietnam

E-mail Address: tcquynh@ued.udn.vn

Corresponding author.

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https://doi.org/10.1142/S0219498821502285Cited by:1 (Source: Crossref)

Abstract

In this paper, by taking the class of all $C 3$ $C 3$ (or $D 3$ $D 3$ ) right $R$ $R$ -modules for general envelopes and covers, we characterize a semisimple artinian ring (or a right perfect ring) via $D 3$ $D 3$ -covers (or $D 3$ $D 3$ -envelopes) and a right $V$ $V$ -ring (or a right noetherian $V$ $V$ -ring) via $C 3$ $C 3$ -covers (or $C 3$ $C 3$ -envelopes). By using isosimple-projective preenvelope, we obtained that if $R$ $R$ is a semiperfect right FGF ring (or left coherent ring), then every isosimple right $R$ $R$ -module has a projective cover. Moreover, we also characterize semihereditary serial rings (respectively, hereditary artinian serial rings) in terms of epic flat (respectively, projective) envelopes.

Communicated by A. Leroy

Keywords:

AMSC: 16D50, 16U60, 16W20

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