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
We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the ...We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the following results:(1)When d>1,any almost complete cluster-tilting object in d-cluster category has only one complement.(2)Cluster-tilting objects in d-cluster categories are induced by tilting modules over some hereditary algebras.We also give a condition for a tilting module to induce a cluster-tilting object in a d-cluster category.(3)A 3-cluster category of finite type admits a cluster-tilting object if and only if its type is A1,A3,D2n-1(n>2).(4)The(2m+1)-cluster category of type D2n-1 admits a cluster-tilting object such that its endomorphism algebra is self-injective,and its stable category is equivalent to the(4m+2)-cluster category of type A4mn-4m+2n-1.展开更多
We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let...We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let D'and D"be subcategories of modΛand modΛ"respectively.For any n,m≥0,under some conditions,we get dimΩ^(k)(D)≤dimΩ^(n)(D')+dimΩ^(m)(D")+1,where k=max{m,n}and D is the subcategory of modΛglued by D'and D";moreover,we give a sufficient condition such that the converse inequality holds true.As applications,some results for Igusa-Todorov subcategories and syzygy finite sub categories are obtained.展开更多
In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni cha...In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an extriangulated category.展开更多
引入局部条件并半格 (简记为 L cusl)及其理想完备化等概念 .证明了 :任一代数 L domain的紧元集是 L cusl;任一代数 L domain是其紧元集赋予 Alexandrov拓扑时的 Sober化 ;任一 L cusl的理想完备化是代数 L domain,从而得到了代数 L do...引入局部条件并半格 (简记为 L cusl)及其理想完备化等概念 .证明了 :任一代数 L domain的紧元集是 L cusl;任一代数 L domain是其紧元集赋予 Alexandrov拓扑时的 Sober化 ;任一 L cusl的理想完备化是代数 L domain,从而得到了代数 L domain的表示定理 .还证明了 Scott连续映射为态射的代数 L domain范畴为 L cusl与单调映射作成的范畴的反射子范畴 .展开更多
目的探讨甲状腺BethesdaⅢ类(AUS/FLUS)结节的诊断原因,以及亚分类在预测结节恶性风险(risk of malignancy,ROM)中的价值。方法收集356例BethesdaⅢ结节患者,对其诊断原因,ROM及亚分类进行总结分析。结果在97例手术切除标本中,72例恶性...目的探讨甲状腺BethesdaⅢ类(AUS/FLUS)结节的诊断原因,以及亚分类在预测结节恶性风险(risk of malignancy,ROM)中的价值。方法收集356例BethesdaⅢ结节患者,对其诊断原因,ROM及亚分类进行总结分析。结果在97例手术切除标本中,72例恶性肿瘤均为甲状腺乳头状癌(papillary thyroid carcinoma,PTC),BethesdaⅢ类的ROM为74.2%。影响PTC诊断的主要原因有病灶小、穿刺细胞量稀少、缺乏乳头状结构及细胞核特征不典型;次要原因有间质显著纤维化或钙化、涂片不合格、固定不当、染色不佳及细胞学诊断经验欠缺等。BethesdaⅢ类的亚分类:132例为低风险组,其中12例手术切除,ROM为8.3%;122例为高风险组,其中70例手术切除,ROM为92.9%;102例为中风险组,其中15例手术切除,ROM为40.0%;高风险组和低/中风险组之间的差异有统计学意义(P<0.05)。结论BethesdaⅢ类的诊断具有一定的主观性和经验性,而对BethesdaⅢ类结节进行风险相关的亚分类,有助于实现更好的ROM分层并改善此类病变的临床管理。展开更多
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.
文摘We consider the existence of cluster-tilting objects in a d-cluster category such that its endomorphism algebra is self-injective,and also the properties for cluster-tilting objects in d-cluster categories.We get the following results:(1)When d>1,any almost complete cluster-tilting object in d-cluster category has only one complement.(2)Cluster-tilting objects in d-cluster categories are induced by tilting modules over some hereditary algebras.We also give a condition for a tilting module to induce a cluster-tilting object in a d-cluster category.(3)A 3-cluster category of finite type admits a cluster-tilting object if and only if its type is A1,A3,D2n-1(n>2).(4)The(2m+1)-cluster category of type D2n-1 admits a cluster-tilting object such that its endomorphism algebra is self-injective,and its stable category is equivalent to the(4m+2)-cluster category of type A4mn-4m+2n-1.
基金Supported by NSFC(Grant Nos.11971225,12171207,12001168)Henan University of Engineering(Grant Nos.DKJ2019010,XTYR-2021JZ001)the Key Research Project of Education Department of Henan Province(Grant No.21A110006)。
文摘We investigate the behavior of the extension dimension of subcategories of abelian categories under recollements.LetΛ',Λ,Λ"be art in algebras such that(modΛ',mod A,modΛ")is a recollement,and let D'and D"be subcategories of modΛand modΛ"respectively.For any n,m≥0,under some conditions,we get dimΩ^(k)(D)≤dimΩ^(n)(D')+dimΩ^(m)(D")+1,where k=max{m,n}and D is the subcategory of modΛglued by D'and D";moreover,we give a sufficient condition such that the converse inequality holds true.As applications,some results for Igusa-Todorov subcategories and syzygy finite sub categories are obtained.
基金supported by the National Natural Science Foundation of China(Nos.12101344,11371196)the Shan Dong Provincial Natural Science Foundation of China(No.ZR2015PA001).
文摘In this paper, the authors introduce a new definition of ∞-tilting(resp. cotilting) subcategories with infinite projective dimensions(resp. injective dimensions) in an extriangulated category. They give a Bazzoni characterization of ∞-tilting(resp. cotilting)subcategories. Also, they obtain a partial Auslander-Reiten correspondence between ∞-tilting(resp. cotilting) subcategories and coresolving(resp. resolving) subcategories with an E-projective generator(resp. E-injective cogenerator) in an extriangulated category.
文摘引入局部条件并半格 (简记为 L cusl)及其理想完备化等概念 .证明了 :任一代数 L domain的紧元集是 L cusl;任一代数 L domain是其紧元集赋予 Alexandrov拓扑时的 Sober化 ;任一 L cusl的理想完备化是代数 L domain,从而得到了代数 L domain的表示定理 .还证明了 Scott连续映射为态射的代数 L domain范畴为 L cusl与单调映射作成的范畴的反射子范畴 .
文摘目的探讨甲状腺BethesdaⅢ类(AUS/FLUS)结节的诊断原因,以及亚分类在预测结节恶性风险(risk of malignancy,ROM)中的价值。方法收集356例BethesdaⅢ结节患者,对其诊断原因,ROM及亚分类进行总结分析。结果在97例手术切除标本中,72例恶性肿瘤均为甲状腺乳头状癌(papillary thyroid carcinoma,PTC),BethesdaⅢ类的ROM为74.2%。影响PTC诊断的主要原因有病灶小、穿刺细胞量稀少、缺乏乳头状结构及细胞核特征不典型;次要原因有间质显著纤维化或钙化、涂片不合格、固定不当、染色不佳及细胞学诊断经验欠缺等。BethesdaⅢ类的亚分类:132例为低风险组,其中12例手术切除,ROM为8.3%;122例为高风险组,其中70例手术切除,ROM为92.9%;102例为中风险组,其中15例手术切除,ROM为40.0%;高风险组和低/中风险组之间的差异有统计学意义(P<0.05)。结论BethesdaⅢ类的诊断具有一定的主观性和经验性,而对BethesdaⅢ类结节进行风险相关的亚分类,有助于实现更好的ROM分层并改善此类病变的临床管理。
