کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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5771797 | 1630423 | 2017 | 31 صفحه PDF | دانلود رایگان |
We introduce and study the new concepts of cosilting complexes, cosilting modules and AIR-cotilting 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 AIR-tilting modules, silting modules and quasi-tilting modules are different. Further, we show that there are bijections between the following four classes (1) equivalence classes of AIR-cotilting (resp., cosilting, quasi-cotilting) modules, (2) equivalence classes of 2-term cosilting complexes, (3) torsion-free cover classes and (4) 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.
Journal: Journal of Algebra - Volume 491, 1 December 2017, Pages 1-31