Let A be an abelian category,and(X,Z,Y)be a complete hereditary cotorsion triple.We introduce the definition of n-Y-cotilting subcategories of A,and give a characterization of n-Y-cotilting subcategories,which is simi...Let A be an abelian category,and(X,Z,Y)be a complete hereditary cotorsion triple.We introduce the definition of n-Y-cotilting subcategories of A,and give a characterization of n-Y-cotilting subcategories,which is similar to Bazzoni characterization of n-cotilting modules.As an application,we prove that if GP is n-GI-cotilting over a virtually Gorenstein ring R,then R is an n-Gorenstein ring,where GP denotes the subcategory of Gorenstein projective R-modules and GI denotes the subcategory of Gorenstein injective R-modules.Furthermore,we investigate n-costar subcategories over arbitrary ring R,and the relationship between n-Icotilting subcategories with respect to cotorsion triple(P,R-Mod,I)and n-costar subcategories,where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.展开更多
In this paper, we introduce the definition of n-star subcategories, which is a generalization of n-star modules and n-C-star modules. We give some characterizations of n-star subcategories, and prove that M is an n-P-...In this paper, we introduce the definition of n-star subcategories, which is a generalization of n-star modules and n-C-star modules. We give some characterizations of n-star subcategories, and prove that M is an n-P-tilting subcategory with respect to cotorsion triple(P, R-Mod, I), if and only if M is an n-star subcategory with I ■Pres^(n)(M), where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.展开更多
Let A be an abelian category,T a self-orthogonal subcategory of A and each object in T admit finite projective and injective dimensions.If the left Gorenstein subcategory lG(T)equals to the right orthogonal class of T...Let A be an abelian category,T a self-orthogonal subcategory of A and each object in T admit finite projective and injective dimensions.If the left Gorenstein subcategory lG(T)equals to the right orthogonal class of T and the right Gorenstein subcategory rG(T)equals to the left orthogonal class of T,we prove that the Gorenstein subcategory G(T)equals to the intersection of the left orthogonal class of T and the right orthogonal class of T,and prove that their stable categories are triangle equivalent to the relative singularity category of A with respect to T.As applications,let R be a left Noetherian ring with finite left self-injective dimension and _(R)C_(S) a semidualizing bimodule,and let the supremum of the flat dimensions of all injective left R-modules be finite.We prove that if RC has finite injective(or flat)dimension and the right orthogonal class of C contains R,then there exists a triangle-equivalence between the intersection of C-Gorenstein projective modules and Bass class with respect to C,and the relative singularity category with respect to C-projective modules.Some classical results are generalized.展开更多
We show that the torsion module Tor_(j)^(R)(R/a,H_(a)^(i)(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism Tor_(s-t)^(R)(R/a,X)≅Tor_(s)^(R)(R/a,H_(a)^(t)(X))in some c...We show that the torsion module Tor_(j)^(R)(R/a,H_(a)^(i)(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism Tor_(s-t)^(R)(R/a,X)≅Tor_(s)^(R)(R/a,H_(a)^(t)(X))in some case.As an application,the Betti number of a complex X in a prime ideal p can be computed by the Betti number of the local cohomology modules of X in p.展开更多
U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admittin...U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admitting reflections by using U_(S)-admitting determined sets.展开更多
目的分析MRI的乳腺影像报告和数据系统(breast imaging reporting and data system,BI-RADS-MRI)4类病例乳腺癌阳性预测值(positive predictive value,PPV),初步探讨其亚分类。方法回顾性总结BI-RADS-MRI4类286例患者的MRI资料,以...目的分析MRI的乳腺影像报告和数据系统(breast imaging reporting and data system,BI-RADS-MRI)4类病例乳腺癌阳性预测值(positive predictive value,PPV),初步探讨其亚分类。方法回顾性总结BI-RADS-MRI4类286例患者的MRI资料,以病理及随访结果为金标准,统计该类病例活检率及PPV,并用Logistic回归法分析各征象的PPV和优势比(OR)。结果 BI-RADS-MRI 4类活检率为75.5%,PPV为30.6%。不规则型肿块呈不均匀强化,平台型或流出型曲线的PPV为0.56;毛刺肿块,强化均匀的PPV为0.45;圆形/椭圆形肿块,边缘光滑,强化均匀的PPV为0.11。病灶呈导管/段样分布、不均匀强化的PPV为0.35;病灶呈局灶/区域/广泛分布、强化均匀的PPV为0.22。结论 PPV能初步对BI-RADS-MRI 4类行亚分类,但仍需进一步研究。展开更多
基金Supported by Research Project in Institutions of Higher Learning in Gansu Province(Grant No.2019B-224)Innovation Fund Project of Colleges and Universities in Gansu Province(Grant No.2020A-277)。
文摘Let A be an abelian category,and(X,Z,Y)be a complete hereditary cotorsion triple.We introduce the definition of n-Y-cotilting subcategories of A,and give a characterization of n-Y-cotilting subcategories,which is similar to Bazzoni characterization of n-cotilting modules.As an application,we prove that if GP is n-GI-cotilting over a virtually Gorenstein ring R,then R is an n-Gorenstein ring,where GP denotes the subcategory of Gorenstein projective R-modules and GI denotes the subcategory of Gorenstein injective R-modules.Furthermore,we investigate n-costar subcategories over arbitrary ring R,and the relationship between n-Icotilting subcategories with respect to cotorsion triple(P,R-Mod,I)and n-costar subcategories,where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.
基金Supported by the 2020 Scientific Research Projects in Universities of Gansu Province (Grant No. 2020A-277)。
文摘In this paper, we introduce the definition of n-star subcategories, which is a generalization of n-star modules and n-C-star modules. We give some characterizations of n-star subcategories, and prove that M is an n-P-tilting subcategory with respect to cotorsion triple(P, R-Mod, I), if and only if M is an n-star subcategory with I ■Pres^(n)(M), where P denotes the subcategory of projective left R-modules and I denotes the subcategory of injective left R-modules.
基金Supported by the Project of Natural Science Foundation of Changzhou College of Information Technology(Grant No.CXZK202204Y)the Project of Youth Innovation Team of Universities of Shandong Province(Grant No.2022KJ314)。
文摘Let A be an abelian category,T a self-orthogonal subcategory of A and each object in T admit finite projective and injective dimensions.If the left Gorenstein subcategory lG(T)equals to the right orthogonal class of T and the right Gorenstein subcategory rG(T)equals to the left orthogonal class of T,we prove that the Gorenstein subcategory G(T)equals to the intersection of the left orthogonal class of T and the right orthogonal class of T,and prove that their stable categories are triangle equivalent to the relative singularity category of A with respect to T.As applications,let R be a left Noetherian ring with finite left self-injective dimension and _(R)C_(S) a semidualizing bimodule,and let the supremum of the flat dimensions of all injective left R-modules be finite.We prove that if RC has finite injective(or flat)dimension and the right orthogonal class of C contains R,then there exists a triangle-equivalence between the intersection of C-Gorenstein projective modules and Bass class with respect to C,and the relative singularity category with respect to C-projective modules.Some classical results are generalized.
基金Natural Science Foundation of Gansu Province(23JRRA866)Higher Education Innovation Fund of Gansu Provincial Department of Education(2025A-132)+1 种基金University-level Scientific Research and Innovation Project of Gansu University of Political Science and Law(GZF2024XQN16)Youth Foundation of Lanzhou Jiaotong University(2023023)。
文摘We show that the torsion module Tor_(j)^(R)(R/a,H_(a)^(i)(X))is in a Serre subcategory for the bounded below R-complex X.In addition,we prove the isomorphism Tor_(s-t)^(R)(R/a,X)≅Tor_(s)^(R)(R/a,H_(a)^(t)(X))in some case.As an application,the Betti number of a complex X in a prime ideal p can be computed by the Betti number of the local cohomology modules of X in p.
基金Supported by the National Natural Science Foundation of China(Grant No.12571507)。
文摘U_(S)-admitting spaces,which were introduced by Heckmann,enjoy many nice properties similar to those of the extensively studied well-filtered spaces.In this paper,we present a direct construction of the U_(S)-admitting reflections by using U_(S)-admitting determined sets.
