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学者姓名：姚海楼
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Abstract ：
It is well known that weak n-tilting modules are vital in tilting theory, which are generalizations of n-tilting and n-cotilting modules. The aim of this paper is to give a new characterization of weak n-tilting modules. In order to do that, we introduce the notion of weak n-star modules. We study more deeply the properties of them. Moreover, connections between (co) star and weak n-star modules are given.
Keyword ：
Weak n-star module Weak n-star module Weak n-tilting module Weak n-tilting module eta-Quasi-flat module eta-Quasi-flat module
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| GB/T 7714 | Yuan, Qianqian , Yao, Hailou . A Characterization of Weak n-Tilting Modules [J]. | JOURNAL OF MATHEMATICAL STUDY , 2024 , 57 (2) : 149-163 . |
| MLA | Yuan, Qianqian 等. "A Characterization of Weak n-Tilting Modules" . | JOURNAL OF MATHEMATICAL STUDY 57 . 2 (2024) : 149-163 . |
| APA | Yuan, Qianqian , Yao, Hailou . A Characterization of Weak n-Tilting Modules . | JOURNAL OF MATHEMATICAL STUDY , 2024 , 57 (2) , 149-163 . |
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Abstract ：
In this paper, we introduce and investigate Tor-tilting comodules and weak silting comodules, providing a generalization of the established tilting and silting theories in the comodule category. Our exploration yields a comprehensive understanding of their fundamental properties, including their associated torsion theories. We delve into not only the relations between Tor-tilting and weak silting comodules but also the connections among them and (co) tilting as well as (co) silting comodules. Additionally, we define Tor-tilting coflat comodules and Tor-tilting coflat dimensions. Finally, we explore Tor-tilting and weak silting objects in the morphism category, demonstrating their equivalence.
Keyword ：
Tor-tilting coflat comodule Tor-tilting coflat comodule Weak silting comodule Weak silting comodule Tor-tilting comodule Tor-tilting comodule morphism category morphism category
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| GB/T 7714 | Yuan, Qianqian , Yao, Hailou . Tor-tilting and weak silting theories in comodule categories [J]. | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2024 . |
| MLA | Yuan, Qianqian 等. "Tor-tilting and weak silting theories in comodule categories" . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS (2024) . |
| APA | Yuan, Qianqian , Yao, Hailou . Tor-tilting and weak silting theories in comodule categories . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2024 . |
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Abstract ：
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.
Keyword ：
n-cosilting module n-cosilting module n-silting module n-silting module Weak n-tilting module Weak n-tilting module n-quasi-cotilting module n-quasi-cotilting module Weak n-silting module Weak n-silting module
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| GB/T 7714 | Yuan, Qianqian , Yao, Hailou . Weak Silting Modules [J]. | ALGEBRAS AND REPRESENTATION THEORY , 2024 , 27 (4) : 1681-1707 . |
| MLA | Yuan, Qianqian 等. "Weak Silting Modules" . | ALGEBRAS AND REPRESENTATION THEORY 27 . 4 (2024) : 1681-1707 . |
| APA | Yuan, Qianqian , Yao, Hailou . Weak Silting Modules . | ALGEBRAS AND REPRESENTATION THEORY , 2024 , 27 (4) , 1681-1707 . |
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Abstract ：
We introduce the notions of silting comodules and finitely silting comodules in quasi-finite category, and study some properties of them. We investigate the torsion pair and dualities which are related to finitely silting comodules, and give the equivalences among silting comodules, finitely silting comodules, tilting comodules and finitely tilting comodules.
Keyword ：
duality duality finitely silting comodule finitely silting comodule quasi-finite silting comodule quasi-finite silting comodule finitely tilting comodule finitely tilting comodule torsion pair torsion pair
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| GB/T 7714 | Yuan, Qianqian , Yao, Hailou . Finitely Silting Comodules in Quasi-Finite Comodule Category [J]. | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2023 , 73 (3) : 695-714 . |
| MLA | Yuan, Qianqian 等. "Finitely Silting Comodules in Quasi-Finite Comodule Category" . | CZECHOSLOVAK MATHEMATICAL JOURNAL 73 . 3 (2023) : 695-714 . |
| APA | Yuan, Qianqian , Yao, Hailou . Finitely Silting Comodules in Quasi-Finite Comodule Category . | CZECHOSLOVAK MATHEMATICAL JOURNAL , 2023 , 73 (3) , 695-714 . |
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Abstract ：
Let ?? be a Grothendieck category, ? an infinite regular cardinal. We investigate the ?-purity of ??, and the ?-pure acyclic complexes in C(??). Using the ?-presentable objects, we verify that the class of ?-pure acyclic complexes is a thick subcategory of homotopy category. Then we construct ?-pure derived category naturally. Through some specific constructions, we get that bounded above ?-pure derived categories coincide with specific homotopy categories.
Keyword ：
?-pure acyclic complex ?-pure acyclic complex ?-pure derived category ?-pure derived category ?-Presentable object ?-Presentable object ?-pure projective object ?-pure projective object
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| GB/T 7714 | Wang, Xi , Yao, Hailou , Shen, Lei . ?-pure derived categories of a Grothendieck category [J]. | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2023 . |
| MLA | Wang, Xi 等. "?-pure derived categories of a Grothendieck category" . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS (2023) . |
| APA | Wang, Xi , Yao, Hailou , Shen, Lei . ?-pure derived categories of a Grothendieck category . | JOURNAL OF ALGEBRA AND ITS APPLICATIONS , 2023 . |
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Abstract ：
As generalizations of silting modules and star modules, respectively, the notions and basic properties of Gorenstein weak n-silting and weak n-star modules are given. We mainly show the "triangular relation" in tilting theory is also valid in silting and star theories in the context of Gorenstein homological algebras. We establish more closed connections among silting and tilting, star theories, that is, we investigate relations between Gorenstein weak n-silting, Gorenstein weak n-tilting and Gorenstein weak n-star modules. Based on these relations, we obtain new characterizations of Gorenstein weak n-tilting modules.
Keyword ：
Gorenstein weak n-tilting module Gorenstein weak n-tilting module Gorenstein weak n-star module Gorenstein weak n-star module Gorenstein weak n-silting module Gorenstein weak n-silting module
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| GB/T 7714 | Yuan, Qianqian , Yao, Hailou . Gorenstein Weak n-Silting Modules and Weak n-Star Modules [J]. | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2023 , 49 (5) . |
| MLA | Yuan, Qianqian 等. "Gorenstein Weak n-Silting Modules and Weak n-Star Modules" . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 49 . 5 (2023) . |
| APA | Yuan, Qianqian , Yao, Hailou . Gorenstein Weak n-Silting Modules and Weak n-Star Modules . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2023 , 49 (5) . |
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Abstract ：
首先引入并研究余代数上的Gorenstein弱投射余模；其次利用推出图与左C-余模短正合列给出了弱投射性与Gorenstein弱投射性之间的关系，得到了一个余模是Gorenstein弱投射余模的等价刻画；最后引入n-Gorenstein弱投射余模，证明每个n-Gorenstein弱投射余模是Gorenstein弱投射余模以及若M是弱投射维数有限的n-Gorenstein弱投射余模，则M是弱投射余模等结论。
Keyword ：
Gorenstein弱投射维数 Gorenstein弱投射维数 Gorenstein弱投射余模 Gorenstein弱投射余模 n-Gorenstein弱投射余模 n-Gorenstein弱投射余模
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| GB/T 7714 | 杨龙姣 , 姚海楼 . 余代数上的Gorenstein弱投射余模 [J]. | 山东大学学报(理学版) , 2023 , 58 (08) : 43-47,56 . |
| MLA | 杨龙姣 等. "余代数上的Gorenstein弱投射余模" . | 山东大学学报(理学版) 58 . 08 (2023) : 43-47,56 . |
| APA | 杨龙姣 , 姚海楼 . 余代数上的Gorenstein弱投射余模 . | 山东大学学报(理学版) , 2023 , 58 (08) , 43-47,56 . |
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Abstract ：
In this paper we study the relation between Gorenstein derived and pure derived categories under some conditions. Then, we also study the relation between Gorenstein singularity and pure singularity categories. Furthermore, we describe the bounded Gorenstein derived category by pure projective modules, under a fairly strong assumption on the ring. In the last part of the paper, we study the pure derived category over a hereditary ring.
Keyword ：
Pure derived category Pure derived category Recollement Recollement Gorenstein derived category Gorenstein derived category Gorenstein singularity category Gorenstein singularity category Pure singularity category Pure singularity category Hereditary Hereditary
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| GB/T 7714 | Yan, Meiqi , Yao, Hailou . The Relation Between Gorenstein Derived and Pure Derived Categories [J]. | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2022 , 48 (6) : 3481-3499 . |
| MLA | Yan, Meiqi 等. "The Relation Between Gorenstein Derived and Pure Derived Categories" . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY 48 . 6 (2022) : 3481-3499 . |
| APA | Yan, Meiqi , Yao, Hailou . The Relation Between Gorenstein Derived and Pure Derived Categories . | BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY , 2022 , 48 (6) , 3481-3499 . |
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Abstract ：
We introduce the concepts of higher-dimensional defect functors and n-Auslander-Reiten translations. Then we prove the higher-dimensional Auslander's defect formula for the category of finitely n-copresented comodules over a left semiperfect coal-gebra. Based on this formula, we obtain the higher-dimensional Auslander-Reiten formula for comodule categories.
Keyword ：
comodule comodule coalgebra coalgebra defect defect transpose transpose Auslander-Reiten formula Auslander-Reiten formula
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| GB/T 7714 | Li, Yexuan , Yao, Hailou . ON HIGHER-DIMENSIONAL A USLANDER-REITEN THEORY FOR COMODULE CATEGORIES [J]. | COLLOQUIUM MATHEMATICUM , 2022 , 171 (1) : 79-101 . |
| MLA | Li, Yexuan 等. "ON HIGHER-DIMENSIONAL A USLANDER-REITEN THEORY FOR COMODULE CATEGORIES" . | COLLOQUIUM MATHEMATICUM 171 . 1 (2022) : 79-101 . |
| APA | Li, Yexuan , Yao, Hailou . ON HIGHER-DIMENSIONAL A USLANDER-REITEN THEORY FOR COMODULE CATEGORIES . | COLLOQUIUM MATHEMATICUM , 2022 , 171 (1) , 79-101 . |
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Abstract ：
Let X be an admissible contravariantly finite subcategory of an abelian category A. We show that A has finite global X-resolution dimension if and only if there is a lower recollement of the homotopy category of bounded complexes over X. We also give sufficient conditions such that the recollement (A, B, C) of abelian categories can be lifted to a (lower or upper) recollement of relative derived categories with respect to balance pairs. Finally, we provide some applications.
Keyword ：
balance pairs balance pairs homotopy category homotopy category Contravariantly finite subcategory Contravariantly finite subcategory recollement recollement
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| GB/T 7714 | Hu, Yonggang , Yao, Hailou . The recollements induced by contravariantly finite subcategories [J]. | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES , 2022 , 132 (1) . |
| MLA | Hu, Yonggang 等. "The recollements induced by contravariantly finite subcategories" . | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES 132 . 1 (2022) . |
| APA | Hu, Yonggang , Yao, Hailou . The recollements induced by contravariantly finite subcategories . | PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES , 2022 , 132 (1) . |
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