Gorenstein相对上同调
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摘要
设M,N是左R-模.证明了如果M的X-Gorenstein投射维数有限,N的Y-Gorenstein内射维数有限,则利用M真的左X-Gorenstein投射分解定义的相对上同调群Ext_(X-GP(M,N))~n与N真的右Y-Gorenstein内射分解定义的相对上同调群Ext_(Y-GI(M,N))~n同构.
Let M,N be left R-modules.We proved that if both the X-Gorenstein projective dimension of M and the Y-Gorenstein injective dimension of N were finite,then the relative cohomology group Ext_(X-GP(M,N))~ndefined by aproper left X-Gorenstein projective resolution of M and the relative cohomology group Ext_(Y-GI(M,N))~n defined by aproper right Y-Gorenstein injective resolution of N were isomorphic.
Let M,N be left R-modules.We proved that if both the X-Gorenstein projective dimension of M and the Y-Gorenstein injective dimension of N were finite,then the relative cohomology group Ext_(X-GP(M,N))~ndefined by aproper left X-Gorenstein projective resolution of M and the relative cohomology group Ext_(Y-GI(M,N))~n defined by aproper right Y-Gorenstein injective resolution of N were isomorphic.
引文
[1]Bennis D,Ouardhi K.X-Gorenstein Projective Module[J].Int Math Forum,2010,5(10):487-491.
[2]Enochs E E,Jenda O M G.Gorenstein Injective and Projective Modules[J].Math Z,1995,220(4):611-633.
[3]DING Nanqing,LI Yuanlin,MAO Lixin.Strongly Gorenstein Flat Modules[J].J Aust Math Soc,2009,86(3):323-338.
[4]Bravo D,Gillspie J,Hovey M.The Stable Module Category of a General Ring[J/OL].Cornell University Library,2014-05-22.https://arxiv.org/pdf/1405.5768v1.pdf.
[5]MENG Fanyun,PAN Qunxing.X-Gorenstein Proiective and Y-Gorenstein Injective Modules[J].Hacet J Math Stat,2011,40(4):537-554.
[6]MAO Lixin,DING Nanqing.Gorenstein FP-Injective and Gorenstein Flat Modules[J].J Algebra Appl,2008,7(4):491-506.
[7]Holm H.Gorenstein Derived Functors[J].Proc Amer Math Soc,2004,132(7):1913-1923.
[8]YANG Gang.Homological Properties of Modules over Ding-Chen Rings[J].J Korean Math Soc,2012,49(1):31-47.
[9]ZHANG Chunxia.Relative and Tate Cohomology of Ding Modules and Complexes[J].J Korean Math Soc,2015,52(4):821-838.
[10]GAO Zenghui,WANG Fanggui.Weak Injective and Weak Flat Modules[J].Comm Algebra,2015,43(9):3857-3868.
[11]Enochs E E,Jenda O M G.Relative Homological Algebra[M].Berlin:Walter de Gruyter,2000.
[12]Hartshore R.Algebraic Geometry[M].New York:Springer-Verlag,1977.
[2]Enochs E E,Jenda O M G.Gorenstein Injective and Projective Modules[J].Math Z,1995,220(4):611-633.
[3]DING Nanqing,LI Yuanlin,MAO Lixin.Strongly Gorenstein Flat Modules[J].J Aust Math Soc,2009,86(3):323-338.
[4]Bravo D,Gillspie J,Hovey M.The Stable Module Category of a General Ring[J/OL].Cornell University Library,2014-05-22.https://arxiv.org/pdf/1405.5768v1.pdf.
[5]MENG Fanyun,PAN Qunxing.X-Gorenstein Proiective and Y-Gorenstein Injective Modules[J].Hacet J Math Stat,2011,40(4):537-554.
[6]MAO Lixin,DING Nanqing.Gorenstein FP-Injective and Gorenstein Flat Modules[J].J Algebra Appl,2008,7(4):491-506.
[7]Holm H.Gorenstein Derived Functors[J].Proc Amer Math Soc,2004,132(7):1913-1923.
[8]YANG Gang.Homological Properties of Modules over Ding-Chen Rings[J].J Korean Math Soc,2012,49(1):31-47.
[9]ZHANG Chunxia.Relative and Tate Cohomology of Ding Modules and Complexes[J].J Korean Math Soc,2015,52(4):821-838.
[10]GAO Zenghui,WANG Fanggui.Weak Injective and Weak Flat Modules[J].Comm Algebra,2015,43(9):3857-3868.
[11]Enochs E E,Jenda O M G.Relative Homological Algebra[M].Berlin:Walter de Gruyter,2000.
[12]Hartshore R.Algebraic Geometry[M].New York:Springer-Verlag,1977.