Cosilting complexes and AIR-cotilting modules
发布时间:2015年12月14日
浏览次数:9941
发布者: Xiaoni Tan
主讲人: Jiaqun Wei( Institute of Mathematics, School of Mathematics Sciences Nanjing Normal University)
活动时间: 从 2015-12-25 16:00 到 17:00
场地: Jingchunyuan 78#, Classroom78406
We introduce and study the new concepts of cosilting complexes, cosilting modules and AIRcotilting
modules. We prove that the three concepts AIR-cotilting modules, cosilting modules
and quasi-cotilting modules coincide with each other, in contrast with the dual fact that AIRtilting
modules, silting modules and quasi-tilting modules are different. Further, we show that
there are bijections between the following four classes (1) equivalent classes of AIR-cotilting
(resp., cosilting, quasi-cotilting) modules, (2) equivalent classes of 2-term cosilting complexes,
p3q torsion-free cover classes and p4q torsion-free special precover classes. We also extend a
classical result of Auslander and Reiten on the correspondence between certain contravariantly
finite subcategories and cotilting modules to the case of cosilting complexes.
This is a joint work with Peiyu Zhang.
modules. We prove that the three concepts AIR-cotilting modules, cosilting modules
and quasi-cotilting modules coincide with each other, in contrast with the dual fact that AIRtilting
modules, silting modules and quasi-tilting modules are different. Further, we show that
there are bijections between the following four classes (1) equivalent classes of AIR-cotilting
(resp., cosilting, quasi-cotilting) modules, (2) equivalent classes of 2-term cosilting complexes,
p3q torsion-free cover classes and p4q torsion-free special precover classes. We also extend a
classical result of Auslander and Reiten on the correspondence between certain contravariantly
finite subcategories and cotilting modules to the case of cosilting complexes.
This is a joint work with Peiyu Zhang.