Quasi-cotilting modules and torsion-free classes

被引：4

作者：

Zhang, Peiyu ^{[1
]}

Wei, Jiaqun ^{[2
]}

机构：

[1] Anhui Polytech Univ, Sch Math & Phys, Wuhu, Peoples R China

[2] Nanjing Normal Univ, Sch Math Sci, Nanjing, Jiangsu, Peoples R China

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2019年 / 18卷 / 11期

基金：

中国国家自然科学基金; 美国国家科学基金会;

关键词：

Quasi-cotilting module; torsion-free class; covering class; pure-injective module; cofinendo module; TILTING MODULES;

D O I：

10.1142/S0219498819502141

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that all quasi-cotilting modules are pure-injective and cofinendo. It follows that the class CogenM is always a covering class whenever M is a quasi-cotilting module. Some characterizations of quasi-cotilting modules are given. As a main result, we prove that there is a bijective correspondence between the equivalent classes of quasi-cotilting modules and torsion-free covering classes.

引用

页数：14

共 50 条

[21] On torsion-free modules over valuation domains
Rangaswamy, KM
INTERNATIONAL SYMPOSIUM ON RING THEORY, 2001, : 313 - 328
[22] Tilting Torsion-Free Classes in the Category of Comodules
Yuan Li
Hailou Yao
Bulletin of the Iranian Mathematical Society, 2021, 47 : 553 - 567
[23] Tilting Torsion-Free Classes in the Category of Comodules
Li, Yuan
Yao, Hailou
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2021, 47 (02) : 553 - 567
[24] QUASI-INVARIANTS FOR TORSION-FREE GROUPS
GOETERS, HP
HOUSTON JOURNAL OF MATHEMATICS, 1994, 20 (03): : 381 - 392
[25] TORSION AND TORSION-FREE QUASI-PURE-PROJECTIVE GROUPS
BENABDALLAH, K
BRADLEY, R
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1976, 23 (04): : A429 - A429
[26] NON-FREE PROJECTIVE MODULES FOR TORSION-FREE GROUPS
BERRIDGE, PH
DUNWOODY, MJ
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1979, 19 (JUN): : 433 - 436
[27] TORSION-FREE NILPOTENT GROUPS AND E-MODULES
DUGAS, M
GOBEL, R
ARCHIV DER MATHEMATIK, 1990, 54 (04) : 340 - 351
[28] STRONGLY COTORSION (TORSION-FREE) MODULES AND COTORSION PAIRS
Yan, Hangyu
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2010, 47 (05) : 1041 - 1052
[29] ENDOMORPHISM ALGEBRAS OF MODULES WITH DISTINGUISHED TORSION-FREE ELEMENTS
FILES, ST
JOURNAL OF ALGEBRA, 1995, 178 (01) : 264 - 276
[30] TORSION-FREE COVERS AND COVERS BY SUBMODULES OF FLAT MODULES
GOMEZ, J
TORRECILLAS, B
COMMUNICATIONS IN ALGEBRA, 1991, 19 (03) : 803 - 827

← 1 2 3 4 5 →