给出了Abelian范畴A和复形范畴Ch(A)中X-Gorenstein内射对象及YX-Gorenstein内射对象的定义,其中XA,YX={Y∈Ch(A)|Y是正合复形且KerdnY∈X}。研究了这两类Gorenstein内射对象的同调性质及它们的区别和联系。证明了若X是包含所有内射...给出了Abelian范畴A和复形范畴Ch(A)中X-Gorenstein内射对象及YX-Gorenstein内射对象的定义,其中XA,YX={Y∈Ch(A)|Y是正合复形且KerdnY∈X}。研究了这两类Gorenstein内射对象的同调性质及它们的区别和联系。证明了若X是包含所有内射对象的自正交的满子范畴,则X∈Ch(A)是YX-Gorenstein内射的当且仅当Xi都是X-Gorenstein内射的。在此基础上研究了两类范畴中X-Gorenstein内射维数和YX-Gorenstein内射维数以及它们之间的关系。在一定的条件下,YX-G I dim(X)=Sup{X-G I dim(Xi)|i∈Z}。展开更多
As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generali...As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.展开更多
文摘给出了Abelian范畴A和复形范畴Ch(A)中X-Gorenstein内射对象及YX-Gorenstein内射对象的定义,其中XA,YX={Y∈Ch(A)|Y是正合复形且KerdnY∈X}。研究了这两类Gorenstein内射对象的同调性质及它们的区别和联系。证明了若X是包含所有内射对象的自正交的满子范畴,则X∈Ch(A)是YX-Gorenstein内射的当且仅当Xi都是X-Gorenstein内射的。在此基础上研究了两类范畴中X-Gorenstein内射维数和YX-Gorenstein内射维数以及它们之间的关系。在一定的条件下,YX-G I dim(X)=Sup{X-G I dim(Xi)|i∈Z}。
基金Supported by the National Natural Science Foundation of China（11401476） Supported by the Project for Universities of Gansu Province（2015A-019）
文摘As a proper setting to study Gorenstein projective and injective dimensions of modules via vanishing of Gorenstein Ext-functors, a notion of a generalized Gorenstein ring is introduced, which is a non-trivial generalization of Gorenstein rings. Moreover, a new proof for Bennis and Mahdou's equality of global Gorenstein dimension is given.
基金partially supported by NSFC(Grant Nos.11401339)NSF of Shandong Province of China(Grant No.ZR2014AQ024)+1 种基金Youth FoundationDoctor's Initial Foundation of Qufu Normal University(Xkj201401,BSQD2012042)
