A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to dis...A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to discuss the condition under which the dual of a tilting pair is also a tilting pair. A necessary and sufficient condition of （D（7）, D（C） ） being an n-tilting pair over an Artin algebra for an n-tilting pair （ C, 7） is given. And, a necessary and sufficient condition of （ T^＊, C^＊ ） being an ntilting pair over a selfinjective Artin algebra for an n-tilting pair （C, 7） is also given.展开更多
The notion of a tilting pair Miyashita in 2001. It is a useful tool in cotorsion pairs related to a fixed tilting （covariantly） finite subcategory and a tilting pair were given in this paper. over artin algebras was...The notion of a tilting pair Miyashita in 2001. It is a useful tool in cotorsion pairs related to a fixed tilting （covariantly） finite subcategory and a tilting pair were given in this paper. over artin algebras was introduced by the tilting theory. Approximations and pair were discussed. A eontravariantly eotorsion pair associated with a fixed展开更多
Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh（C）-right Endh（T）-bimodule for a given tilting pairs （C,T） in modh, where A ...Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh（C）-right Endh（T）-bimodule for a given tilting pairs （C,T） in modh, where A is an Artin algebra.展开更多
It was shown recently that the heart of a twin cotorsion pair on an extriangulated category is semi-abelian.In this article,we consider a special class of hearts of twin cotorsion pairs induced by d-cluster tilting su...It was shown recently that the heart of a twin cotorsion pair on an extriangulated category is semi-abelian.In this article,we consider a special class of hearts of twin cotorsion pairs induced by d-cluster tilting subcategories in extriangulated categories.We give a necessary and sufficient condition for such hearts to be abelian.In particular,we can also see that such hearts are hereditary.As an application,this generalizes the work by Liu in the exact case,thereby providing new insights into the triangulated case.展开更多
The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.
基金The National Natural Science Foundation of China (No.10971024)the Specialized Research Fund for the Doctoral Program of Higher Education ( No. 200802860024)+1 种基金the Natural Science Foundation of Jiangsu Province ( No. BK2010393 )Scientific Research Foundation of Guangxi University ( No. XJZ100246)
文摘A module pair （C, T） over an Artin algebra A is called a tilting pair if both C and T are selforthogonal modules and the conditions T e ada C and C ∈ add T hold. The duality on a tilting pair is investigated to discuss the condition under which the dual of a tilting pair is also a tilting pair. A necessary and sufficient condition of （D（7）, D（C） ） being an n-tilting pair over an Artin algebra for an n-tilting pair （ C, 7） is given. And, a necessary and sufficient condition of （ T^＊, C^＊ ） being an ntilting pair over a selfinjective Artin algebra for an n-tilting pair （C, 7） is also given.
文摘The notion of a tilting pair Miyashita in 2001. It is a useful tool in cotorsion pairs related to a fixed tilting （covariantly） finite subcategory and a tilting pair were given in this paper. over artin algebras was introduced by the tilting theory. Approximations and pair were discussed. A eontravariantly eotorsion pair associated with a fixed
基金Supported by the National Natural Science Foundation of China (Grant Nos.1097102410826036)+2 种基金the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No.200802860024)the Natural Science Foundation of Jiangsu Province (Grant No.BK2010393)the Scientific Research Foundation of Guangxi University (Grant No.XJZ100246)
文摘Tilting pair was introduced by Miyashita in 2001 as a generalization of tilting module. In this paper, we construct a tilting left Endh（C）-right Endh（T）-bimodule for a given tilting pairs （C,T） in modh, where A is an Artin algebra.
基金Panyue Zhou was supported by the Hunan Provincial Natural Science Foundation of China(Grant No.2023JJ30008).
文摘It was shown recently that the heart of a twin cotorsion pair on an extriangulated category is semi-abelian.In this article,we consider a special class of hearts of twin cotorsion pairs induced by d-cluster tilting subcategories in extriangulated categories.We give a necessary and sufficient condition for such hearts to be abelian.In particular,we can also see that such hearts are hereditary.As an application,this generalizes the work by Liu in the exact case,thereby providing new insights into the triangulated case.
基金supported by National Natural Science Foundation of China(Grant No.10931006)
文摘The purpose of this paper is to provide the TTF-theories and investigate the comparisons of recollements(one-sided recollements) both induced by the BB-tilting modules.
