相对于余挠对的n-强Gorenstein投射模
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摘要
引入相对于完备遗传的余挠对的n-强Gorenstein投射模,讨论其同调性质;并给出了相对于完备遗传的余挠对的n-强Gorenstein投射模的一些等价刻画.
This paper introduces the n-strongly Gorenstein projective modules with respect to complete and hereditary cotorsion pairs,and discusses their homological properties.Some equivalent characterizations of n-strongly Gorenstein projective modules with respect to cotorsion pairs are given.
This paper introduces the n-strongly Gorenstein projective modules with respect to complete and hereditary cotorsion pairs,and discusses their homological properties.Some equivalent characterizations of n-strongly Gorenstein projective modules with respect to cotorsion pairs are given.
引文
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[4] BENNIS D,MAHDOU N.Strongly Gorenstein projective,injective,and flat modules[J].J Pure Appl Algebra,2007,210(2):437.
[5] BENNIS D,MAHDOU N.A generalization of strongly Gorenstein projective modules[J].J Appl Algebra,2009,8(2):219.
[6] ZHAO Guo-qing,HUANG Z Y.n-strongly Gorenstein projective,injective and flat modules[J].Comm Algebra,2011,39(8):3044.
[7] PAN Qun-xing,CAI Fa-qun.(X,Y)-Gorenstein projective and injective modules[J].Turk J Math,2015,39:81.
[8] XU Ai-ming.Gorenstein modules and Gorenstein model structures[J].Glasgow Math,2017,59:685.
[9] YANG Xiao-yan,CHEN Wen-jing.Relative homologic dimensions and Tate cohomology of complexes with respect to cotorsion pairs[J].Comm Algebra,2017,45(7):2875.
[10] ENOCHS E E,JENDA O M G.Relative Homological Algebra[M].Berlin:Walter de Gruyter,2000.
[11] GARCIA R J R.Covers and Envelopes in the Category of Complexes of Modules[M].Research Notes in Mathematics Vol 407.New York:Chapman and Hall/CRC,1999.
[12] SALCE L.Cotorsion theories for abelian groups[J].Symposia Math,1979,23:11.
[13] GILLESPIE J.The flat stable module category of a coherent ring[J].J Pure Appl Algebra,2017,221(8):2025.
[14] HU Jiang-sheng,XU Ai-ming.On stability of F-Gorenstein flat categories[J].Algebra Colloquium,2016,23(2):251.
[15] HOLM H.Gorenstein homological dimensions[J].J Pure Appl Algebra,2004,189(1):167.
[2] ENOCHS E E,JENDA O M G,TORRECILLAS B.Gorenstein flat modules[J].Nanjing Univ Math Biquart,1993,10:1.
[3] ENOCHS E E,JENDQA O M G.Gorenstein injective and projective modules[J].Math Z,1995,220(1):611.
[4] BENNIS D,MAHDOU N.Strongly Gorenstein projective,injective,and flat modules[J].J Pure Appl Algebra,2007,210(2):437.
[5] BENNIS D,MAHDOU N.A generalization of strongly Gorenstein projective modules[J].J Appl Algebra,2009,8(2):219.
[6] ZHAO Guo-qing,HUANG Z Y.n-strongly Gorenstein projective,injective and flat modules[J].Comm Algebra,2011,39(8):3044.
[7] PAN Qun-xing,CAI Fa-qun.(X,Y)-Gorenstein projective and injective modules[J].Turk J Math,2015,39:81.
[8] XU Ai-ming.Gorenstein modules and Gorenstein model structures[J].Glasgow Math,2017,59:685.
[9] YANG Xiao-yan,CHEN Wen-jing.Relative homologic dimensions and Tate cohomology of complexes with respect to cotorsion pairs[J].Comm Algebra,2017,45(7):2875.
[10] ENOCHS E E,JENDA O M G.Relative Homological Algebra[M].Berlin:Walter de Gruyter,2000.
[11] GARCIA R J R.Covers and Envelopes in the Category of Complexes of Modules[M].Research Notes in Mathematics Vol 407.New York:Chapman and Hall/CRC,1999.
[12] SALCE L.Cotorsion theories for abelian groups[J].Symposia Math,1979,23:11.
[13] GILLESPIE J.The flat stable module category of a coherent ring[J].J Pure Appl Algebra,2017,221(8):2025.
[14] HU Jiang-sheng,XU Ai-ming.On stability of F-Gorenstein flat categories[J].Algebra Colloquium,2016,23(2):251.
[15] HOLM H.Gorenstein homological dimensions[J].J Pure Appl Algebra,2004,189(1):167.