Purely Extending Modules and Their Generalizations

被引：0

作者：

Kumar, Shiv ^{[1
]}

Gupta, Ashok Ji ^{[1
]}

机构：

[1] IIT BHU, Dept Math Sci, Varanasi 221005, India

来源：

KYUNGPOOK MATHEMATICAL JOURNAL | 2023年 / 63卷 / 01期

关键词：

Extending module; Flat module; Purely extending module; Purely Baer module; Purely essentially Baer module; ENDOMORPHISM-RINGS; BAER;

D O I：

10.5666/KMJ.2022.63.1.15

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A purely extending module is a generalization of an extending module. In this paper, we study several properties of purely extending modules and introduce the notion of purely essentially Baer modules. A module M is said to be a purely essentially Baer if the right annihilator in M of any left ideal of the endomorphism ring of M is essential in a pure submodule of M. We study some properties of purely essentially Baer modules and characterize von Neumann regular rings in terms of purely essentially Baer modules.

引用

页码：15 / 27

页数：13

共 17 条

[1] PURELY BAER MODULES AND PURELY RICKART MODULES [J].

Atani, S. Ebrahimi ;

Khoramdel, M. ;

Pishhesari, S. Dolati .

MISKOLC MATHEMATICAL NOTES, 2018, 19 (01) :63-76

[2]

Birkenmeier G.F., 2013, EXTENSIONS RINGS MOD, DOI DOI 10.1007/978-0-387-92716-9

[3] RINGS IN WHICH EVERY COMPLEMENT RIGHT IDEAL IS A DIRECT SUMMAND [J].

CHATTERS, AW ;

HAJARNAVIS, CR .

QUARTERLY JOURNAL OF MATHEMATICS, 1977, 28 (109) :61-80

[4] ENDOMORPHISM-RINGS OF MODULES OVER NON-SINGULAR CS RINGS [J].

CHATTERS, AW ;

KHURI, SM .

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1980, 21 (JUN) :434-444

[5]

Clark J, 1999, TRENDS MATH, P353

[6]

Cohn P.M., 1959, MATH Z, V71, P380

[7] PURE THEORIES [J].

FIELDHOU.DJ .

MATHEMATISCHE ANNALEN, 1969, 184 (01) :1-&

[8]

Goodearl K., 1979, Monographs and Studies in Mathematics, DOI DOI 10.1007/3-540-26370-5-8

[9]

Lam T.Y., 1999, LECT MODULES RINGS G, V189

[10] Modules Whose Endomorphism Rings are Von Neumann Regular [J].

Lee, Gangyong ;

Rizvi, S. Tariq ;

Roman, Cosmin .

COMMUNICATIONS IN ALGEBRA, 2013, 41 (11) :4066-4088

← 1 2 →