Modules with ADS-(pre)envelopes and ADS-(pro)covers

被引：3

作者：

Truong Cong Quynh ^{[1
,2
]}

Kosan, M. Tamer ^{[3
]}

机构：

[1] Ton Duc Thang Univ, Dept Management Sci & Technol Dev, Ho Chi Minh City, Vietnam

[2] Ton Duc Thang Univ, Fac Math & Stat, Ho Chi Minh City, Vietnam

[3] Gebze Tech Univ, Dept Math, TR-41400 Kocaeli, Turkey

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2018年 / 17卷 / 05期

关键词：

ADS module; (pre)envelope; (pre)cover; Noetherian ring; V-ring; ADS MODULES; RINGS;

D O I：

10.1142/S0219498818500962

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper focusses on the question of when modules have ADS- preenvelopes and covers. For a ring R, it is proved that every ADS module over R is injective if and only if every right R-module has an ADS-(pre)envelope (an ADS-(pre)cover). In this paper, we also introduce a generalization of ADS modules stated in terms of their invariance under certain automorphisms of their envelopes.

引用

页数：15

共 9 条

[1] ADS modules [J].

Alahmadi, Adel ;

Jain, S. K. ;

Leroy, Andre .

JOURNAL OF ALGEBRA, 2012, 352 (01) :215-222

[2]

Anderson F. W., 1974, Rings and Categories of Modules

[3]

Enochs E. E., 2011, RELATIVE HOMOLOGICAL, V1

[4] Modules invariant under automorphisms of their covers and envelopes [J].

Guil Asensio, Pedro A. ;

Tutuncu, Derya Keskin ;

Srivastava, Ashish K. .

ISRAEL JOURNAL OF MATHEMATICS, 2015, 206 (01) :457-482

[5] Nilpotent-invariant modules and rings [J].

Kosan, M. Tamer ;

Truong Cong Quynh .

COMMUNICATIONS IN ALGEBRA, 2017, 45 (07) :2775-2782

[6] MODULES WHICH ARE INVARIANT UNDER AUTOMORPHISMS OF THEIR INJECTIVE HULLS [J].

Lee, Tsiu-Kwen ;

Zhou, Yiqiang .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2013, 12 (02)

[7]

Mohammad S., 1990, CONTINUOUS DISCRETE, V147

[8] On automorphism-invariant modules [J].

Truong Cong Quynh ;

Kosan, M. Tamer .

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2015, 14 (05)

[9] ON ADS MODULES AND RINGS [J].

Truong Cong Quynh ;

Kosan, M. Tamer .

COMMUNICATIONS IN ALGEBRA, 2014, 42 (08) :3541-3551

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