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Gorenstein n-Cotorsion Modules And Gorenstein n-Cotorsion Dimension[J]. Journal of South China Normal University (Natural Science Edition), 2015, 47(6): 111-115.
Citation: Gorenstein n-Cotorsion Modules And Gorenstein n-Cotorsion Dimension[J]. Journal of South China Normal University (Natural Science Edition), 2015, 47(6): 111-115.

Gorenstein n-Cotorsion Modules And Gorenstein n-Cotorsion Dimension

Funds: 

The National Natural Science Foundation of China

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  • Received Date: March 15, 2015
  • Revised Date: April 26, 2015
  • Let R be a ring, M a left R-modules and n a fixed nonnegative integer.~Recall that M is called Gorenstein n-cotorsion if Ext1R(N,M)=0 for any Gorenstein~n-flat left R-modules N.~In this paper,~we discuss the relative properties of Gorenstein n-cotorsion modules and Gorenstein n-cotorsion dimension of modules and rings over right n-coherent rings.
  • [1] BENNIS D. Rings over which the class of Gorenstein flat modules is closed under extensions[J].Comm. Algebra, 2009, 37:855-868 [2]YANG Gang, LIU Zhongkui.Gorenstein flat covers over GF-closed rings[J].Comm. Algebra, 2012, 40(5):1632-1642 [3] MAO Lixin, DING Nanqing.The cotorsion dimension of modules and rings 2006, 249 : 217-233[J].Abelian Groups, Rings, Modules, and Homological Algebra, 2006, 249:217-233 [4]GAO Zenghui.On Gorenstein cotorsion dimension over GF-closed rings[J].Bull. Korean Math. Soc., 2014, 51(1):173-187 [5]LEE S B.n-coherent rings[J].Comm. Algebra, 2002, 30(3):1119-1126 [6] SELVARAJ C, UDHAYAKUMAR R, UMAMAHESWARAN A.Gorenstein n-flat modules and their covers[J].Asia-European Journal of Mathematics, 2014, 7(3):- [7] ENOCHS E E, JENDA O M G.Relative homological algebra[M]. Belin : Walter de Gruyter, 2000. [8] DING Nanqing.On envelopes with the Unique Mapping Property[J]. [J].Comm. Algebra, 1996, 24:1459-1470 [9]ENOCHS E E, JENDA O M G, LOPEZ-RAMOS J A.The existence of Gorenstein flat covers[J].Math. Scand, 2004, 94(1):46-62 [10] HOIM H.Gorenstein homological dimensions[J]. [J].Journal of Pure Application Algebra, 2004, 189:167-193 [11] 佟文廷.同调代数引论[M].北京:高等教育出版社, 1998.

    [1] BENNIS D. Rings over which the class of Gorenstein flat modules is closed under extensions[J].Comm. Algebra, 2009, 37:855-868 [2]YANG Gang, LIU Zhongkui.Gorenstein flat covers over GF-closed rings[J].Comm. Algebra, 2012, 40(5):1632-1642 [3] MAO Lixin, DING Nanqing.The cotorsion dimension of modules and rings 2006, 249 : 217-233[J].Abelian Groups, Rings, Modules, and Homological Algebra, 2006, 249:217-233 [4]GAO Zenghui.On Gorenstein cotorsion dimension over GF-closed rings[J].Bull. Korean Math. Soc., 2014, 51(1):173-187 [5]LEE S B.n-coherent rings[J].Comm. Algebra, 2002, 30(3):1119-1126 [6] SELVARAJ C, UDHAYAKUMAR R, UMAMAHESWARAN A.Gorenstein n-flat modules and their covers[J].Asia-European Journal of Mathematics, 2014, 7(3):- [7] ENOCHS E E, JENDA O M G.Relative homological algebra[M]. Belin : Walter de Gruyter, 2000. [8] DING Nanqing.On envelopes with the Unique Mapping Property[J]. [J].Comm. Algebra, 1996, 24:1459-1470 [9]ENOCHS E E, JENDA O M G, LOPEZ-RAMOS J A.The existence of Gorenstein flat covers[J].Math. Scand, 2004, 94(1):46-62 [10] HOIM H.Gorenstein homological dimensions[J]. [J].Journal of Pure Application Algebra, 2004, 189:167-193 [11] 佟文廷.同调代数引论[M].北京:高等教育出版社, 1998.

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