ON (m, n)-QUASI-INJECTIVE MODULES

被引：0

作者：

Zhu, Z. M. ^{[1
]}

Chen, J. L. ^{[2
]}

Zhang, X. X. ^{[2
]}

机构：

[1] Jiaxing Univ, Dept Math, Jiaxing 314001, Zhejiang, Peoples R China

[2] Southeast Univ, Dept Math, Nanjing 210096, Jiangsu, Peoples R China

来源：

ACTA MATHEMATICA UNIVERSITATIS COMENIANAE | 2005年 / 74卷 / 01期

关键词：

(m; n)-quasi-injective modules; Kasch modules;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let R be a ring. For two fixed positive integers m and n, an R-module M is called (m, n)-quasi-injective if each R-homomorphism from an n-generated submodule of M-m to M extends to one from M-m to M. It is showed that M-R is (m,n)-quasi-injective if and only if the right R-nxn-module M-mxn is principally quasi-injective. Many properties of (m, n)-injective rings and principally quasi-injective modules are extended to these modules. Moreover, some properties of (m, n)-quasi-injective Kasch modules are investigated.

引用

页码：25 / 36

页数：12

共 9 条

[1]

Albu T., 1997, ADV RING THEORY, P1

[2]

ANDERSON FW, 1974, GTM, V13

[3] On (m, n)-injectivity of modules [J].

Chen, JL ;

Ding, NQ ;

Li, YL ;

Zhou, YQ .

COMMUNICATIONS IN ALGEBRA, 2001, 29 (12) :5589-5603

[4]

GOODEARL KR, 1976, RING THEORY NONSINGU

[5] Principally quasi-injective modules [J].

Nicholson, WK ;

Park, JK ;

Yousif, MF .

COMMUNICATIONS IN ALGEBRA, 1999, 27 (04) :1683-1693

[6] On a theorem of Camillo [J].

Nicholson, WK ;

Yousif, MF .

COMMUNICATIONS IN ALGEBRA, 1995, 23 (14) :5309-5314

[7] PRINCIPALLY INJECTIVE-RINGS [J].

NICHOLSON, WK ;

YOUSIF, MF .

JOURNAL OF ALGEBRA, 1995, 174 (01) :77-93

[8]

RAMAMURTHI V. S., 1973, J AUSTRAL MATH SOC, V16, P239, DOI DOI 10.1017/S1446788700014294

[9]

Wisbauer R., 1991, FDN MODULE RING THEO, V3

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