When every endomorphism of a Σ-injective module is a sum of two commuting automorphisms

被引：1

作者：

Siddique, Feroz ^{[1
,2
]}

机构：

[1] Univ Wisconsin Coll, Dept Math, Madison, WI 53711 USA

[2] Univ Wisconsin Eau Claire Barron Cty, Dept Math, Rice Lake, WI 54868 USA

来源：

RINGS, MODULES AND CODES | 2019年 / 727卷

关键词：

Units; Sigma-injective modules; injective modules; directly finite; RINGS;

D O I：

10.1090/conm/727/14646

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is well known that if M is an injective module then each endomorphism of M is a sum of two automorphisms if and only if End(M) has no homomorphic image isomorphic to the field of two elements. In this paper we show that if M is a Sigma-injective module such that each homomorphism of M is a sum of two commuting automorphisms then M must be directly finite.

引用

页码：349 / 355

页数：7

共 24 条

[1]

Bass H., 1962, Trans. Amer. Math. Soc, V102, P18

[2] New characterization of Σ-injective modules [J].

Beidar, K. I. ;

Jain, S. K. ;

Srivastava, Ashish K. .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2008, 136 (10) :3461-3466

[3]

CAILLEAU A, 1969, CR ACAD SCI A MATH, V269, P997

[4] DEDEKIND-FINITE STRONGLY CLEAN RINGS [J].

Camillo, Victor ;

Dorsey, Thomas J. ;

Nielsen, Pace P. .

COMMUNICATIONS IN ALGEBRA, 2014, 42 (04) :1619-1629

[5]

Cartan H., 1956, Homological algebra

[6]

Castgan F., 1968, Pac. J. Math, V27

[7]

Dieudonne J, 1948, COMMENT MATH HELV, V21, P154

[8] RINGS WITH ASCENDING CONDITION ON ANNIHILATORS [J].

FAITH, C .

NAGOYA MATHEMATICAL JOURNAL, 1966, 27 (01) :179-&

[9]

Faith C., 1967, LECT NOTES MATH, V49

[10]

FREEDMAN H, 1968, J LONDON MATH SOC, V43, P305

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