Characterizing Baer modules over τq-semisimple rings: An extension of Baer's problem

被引：0

作者：

Zhang, Xiaolei ^{[1
,2
]}

Kim, Hwankoo ^{[3
]}

机构：

[1] Tianshui Normal Univ, Sch Math & Stat, Tianshui 741001, Peoples R China

[2] Shandong Univ Technol, Sch Math & Stat, Zibo 255000, Peoples R China

[3] Hoseo Univ, Div Comp Engn, Asan, South Korea

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2025年

基金：

新加坡国家研究基金会;

关键词：

Baer splitting problem; Baer module; tau(q)-semisimple ring;

D O I：

10.1142/S0219498826502038

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this note, we investigate the Baer splitting problem over commutative rings. In particular, we show that if a commutative ring R is tau(q)-semisimple, then every Baer R-module is projective.

引用

页数：10

共 17 条

[1]

Angeleri Hugel L, 2008, T AM MATH SOC, V360, P2409

[2] The subgroup of the elements of finite order of an Abelian group [J].

Baer, R .

ANNALS OF MATHEMATICS, 1936, 37 :766-781

[3] BAER MODULES OVER DOMAINS [J].

EKLOF, PC ;

FUCHS, L ;

SHELAH, S .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 322 (02) :547-560

[4] BAER MODULES OVER VALUATION DOMAINS [J].

EKLOF, PC ;

FUCHS, L .

ANNALI DI MATEMATICA PURA ED APPLICATA, 1988, 150 :363-373

[5]

FUCHS L, 2001, MODULES NONNOETHERIA

[6] Covers and envelopes related to divisibility [J].

Fuchs, Laszlo .

BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA, 2023, 29 (03)

[7]

Gobel R., 2012, DEGRUYTER EXPOSITION, V41

[8]

Golan J. S., 1986, Pitman Monographs and Surveys in Pure and Applied Mathematics, V29

[9]

Kaplansky I, 1962, Arch. Math., V13, P341

[10] THE MINIMAL PRIME SPECTRUM OF A REDUCED RING [J].

MATLIS, E .

ILLINOIS JOURNAL OF MATHEMATICS, 1983, 27 (03) :353-391

← 1 2 →