ON A GENERALIZATION OF TILTING MODULES

被引:6
作者
Zhang, Xiaoxiang [1 ]
Yao, Lingling [1 ]
机构
[1] Southeast Univ, Dept Math, Nanjing 210096, Peoples R China
关键词
Cotilting module; Tilting module; Torsion theory; Tor-tilting module;
D O I
10.1080/00927870902828983
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let R be a ring. A right R-module U is called Tor-tilting if Cogen (U+) = Ker Tor(1)(R)(U, -), where U+ = Hom(Z)(U, Q/Z), Cogen (U+) is the class of left R-modules cogenerated by U+ and Ker Tor(1)(R)(U, -) consists of modules M-R such that Tor(1)(R)(U, M) = 0. Some examples and characterizations of Tor-tilting modules are given. Among others, it is shown that U-R is Tor-tilting if and only if U+ is cotilting. Moreover, both tilting modules and completely faithful flat modules are proved to be Tor-tilting. The torsion theory induced by a Tor-tilting module is also investigated.
引用
收藏
页码:4316 / 4324
页数:9
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