Weak Silting Modules

It is well-established that weak n -tilting modules serve as generalizations of both n -tilting and n -cotilting modules. The primary objective of this paper is to delineate the characterizations of weak n -silting modules and elaborate on their applications. Specifically, we aim to establish the &q...

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Bibliographic Details
Published in:Algebras and representation theory 2024-08, Vol.27 (4), p.1681-1707
Main Authors: Yuan, Qianqian, Yao, Hailou
Format: Article
Language:English
Subjects:
Associative Rings and Algebras
Commutative Rings and Algebras
Mathematics
Mathematics and Statistics
Modules
Non-associative Rings and Algebras
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Summary:It is well-established that weak n -tilting modules serve as generalizations of both n -tilting and n -cotilting modules. The primary objective of this paper is to delineate the characterizations of weak n -silting modules and elaborate on their applications. Specifically, we aim to establish the "triangular relation" within the framework of silting theory in a module category, and provide novel characterizations of weak n -tilting modules. Furthermore, we delve into the properties of n -(co)silting modules and their interrelations with some other types of modules. Additionally, we explore the conditions under which a weak n -silting module can be classified as partial n -silting, weak n -tilting, or partial n -tilting. Notably, we establish and prove that Bazzoni’s renowned characterization of pure-injectivity for cotilting modules remains valid for weak n -silting modules with respect to F T . Lastly, we investigate weak n -silting and weak n -tilting objects in a morphism category.
ISSN:1386-923X
1572-9079
DOI:10.1007/s10468-024-10276-8