Model Structures on Categories of Complexes Over Ding-Chen Rings

REFERENCES

• Avramov , L. L. , Foxby , H.-B. ( 1991 ). Homological dimensions of unbounded complexes . J. Pure Appl. Algebra 71 : 129 – 155 .
   Web of Science ®Google Scholar
• Cortés Izurdiaga , M. , Estrada , S. , Guil Asensio , P. A. ( 2012 ). A Quillen model structure approach to the finitistic dimension conjectures . Math. Scand. 285 ( 7 ): 821 – 833 .
   Google Scholar
• Damiano , R. F. ( 1979 ). Coflat rings and modules . Pacific J. Math. 81 ( 2 ): 349 – 369 .
   Web of Science ®Google Scholar
• Ding , N. Q. , Chen , J. L. ( 1993 ). The flat dimensions of injective modules . Manuscripta Math. 78 ( 2 ): 165 – 177 .
   Web of Science ®Google Scholar
• Ding , N. Q. , Chen , J. L. (1996). Coherent rings with finite self-FP-injective dimension. Comm. Algebra 24:2963–2980.
   Web of Science ®Google Scholar
• Ding , N. Q. , Li , Y. L. , Mao , L. X. ( 2009 ). Strongly Gorenstein flat modules . J. Aust. Math. Soc. 86 ( 3 ): 323 – 338 .
   Web of Science ®Google Scholar
• Ding , N. Q. , Mao , L. X. ( 2008 ). Gorenstein FP-injective and Gorenstein flat modules . J. Algebra Appl. 7 ( 4 ): 491 – 506 .
   Web of Science ®Google Scholar
• Ding , N. Q. , Mao , L. X. ( 2005 ). Reletive FP-projective modules . Comm. Algebra 33 : 1587 – 1602 .
   Web of Science ®Google Scholar
• Enochs , E. E. , Estrada , S. , García Rozas , J. R. ( 2008 ). Locally projective monoidal model structure for complexes of quasi-coherent sheaves an P 1(k) . J. London Math. Soc. 77 ( 2 ): 253 – 269 .
   Google Scholar
• Enochs , E. E. , Estrada , S. , Torrecillas , B. ( 2005 ). Gorenstein flat covers and Gorenstein cotorsion modules over integral group rings . Algebras Repr. Theory 8 : 525 – 539 .
   Web of Science ®Google Scholar
• Enochs , E. E. , García Rozas , J. R. ( 1997 ). Tensor products of complexes . Math. J. Okayama Univ. 39 : 17 – 39 .
   Google Scholar
• Enochs , E. E. , García Rozas , J. R. ( 1988 ). Flat covers of complexes . J. Algebra 210 : 86 – 102 .
   Web of Science ®Google Scholar
• Enochs , E. E. , García Rozas , J. R. ( 1988 ). Gorenstein injective and projective complexes . Comm. Algebra 26 : 1657 – 1674 .
   Web of Science ®Google Scholar
• Enochs , E. E. , Iacob , A. ( 2006 ). The ℵ 1-product of DG-injective complexes . Proc. Edinb. Math. Soc. 49 : 257 – 266 .
   Web of Science ®Google Scholar
• Enochs , E. E. , Jenda , O. M. G. ( 1995 ). Gorenstein injective and projective modules . Math. Z. 220 ( 4 ): 611 – 633 .
   Web of Science ®Google Scholar
• Enochs , E. E. , Jenda , O. M. G. ( 2000 ). Relative Homological Algebra . Berlin : Walter De Gruyter .
   Google Scholar
• Enochs , E. E. , Jenda , O. M. G. , Torrecillas , B. ( 1993 ). Gorenstein flat modules . J Nanjing Univ Math Biquarterly 10 ( 1 ): 1 – 9 .
   Google Scholar
• Enochs , E. E. , López Ramos , J. A. ( 2001 ). Gorenstein Flat Modules . Huntington , NY : Nova Scientific Publishers .
   Google Scholar
• Gillespie , J. ( 2004 ). The flat model structure on Ch(R) . Trans. Amer. Math. Soc. 356 ( 8 ): 3369 – 3390 .
   Web of Science ®Google Scholar
• Gillespie , J. ( 2010 ). Model structures on modules over Ding–Chen rings . Homology, Homotopy Appl. 12 ( 1 ): 61 – 73 .
   Web of Science ®Google Scholar
• Gillespie , J. , Hovey , M. ( 2010 ). Gorenstein model structures and generalized derived categories . Proc. Edinb. Math. Soc. 53 : 675 – 696 .
   Web of Science ®Google Scholar
• García Rozas , J. R. ( 1999 ). Covers and Envelope in the Category of Complexes of Modules. Research Notes in Mathematics , Vol. 407 , New York : Chapman and Hall/CRC .
   Google Scholar
• Holm , H. ( 2004 ). Gorenstein homological dimensions . J. Pure Appl. Algebra 189 : 167 – 193 .
   Web of Science ®Google Scholar
• Hovey , M. ( 2002 ). Cotorsion pairs, model category structures, and representation theory . Math. Z. 241 : 553 – 592 .
   Web of Science ®Google Scholar
• Hovey , M. ( 1999 ). Model Categories . Providence , RI : American Mathematical Society .
   Google Scholar
• Mao , L. X. , Ding , N. Q. ( 2007 ). Envelopes and covers by modules of finite FP-injective and flat dimensions . Comm. Algebra 35 : 833 – 849 .
   Web of Science ®Google Scholar
• Mao , L. X. , Ding , N. Q. ( 2008 ). Gorenstein FP-injective and Gorenstein flat modules . J. Algebra Appl. 7 ( 4 ): 491 – 506 .
   Web of Science ®Google Scholar
• Salce , L. ( 1979 ). Cotorsion theories for abelian groups . Sympos Math. Vol XIII : 11 – 32 .
   Google Scholar
• Stenström , B. ( 1970 ). Coherent rings and FP-injective modules . J. Lond. Math. Soc. 2 ( 2 ): 323 – 329 .
   Web of Science ®Google Scholar
• Spaltenstein , N. ( 1988 ). Resolutions of unbounded complexes . Compositio Math. 65 : 121 – 154 .
   Web of Science ®Google Scholar
• Wang , Z. P. , Liu , Z. K. (2011). FP-injective complexes and FP-injective dimension of complexes. J. Aust. Math. Soc. 91:163–187.
   Web of Science ®Google Scholar
• Xu , J. Z. ( 1996 ). Flat Covers of Modules. Lecture Notes in Math. 1634 .
   Google Scholar
• Yang , G. ( 2011 ). Gorenstein projective, injective and flat complexes . Acta Math. sinica, Chinese Series 54 ( 3 ): 451 – 460 .
   Google Scholar
• Yang , G. , Liu , Z. K. ( 2012 ). Cotorsion pairs and model structures on Ch(R) . Proc. Edinb. Math. Soc. 54 : 783 – 797 .
   Web of Science ®Google Scholar
• Yang , G. , Liu , Z. K. , Liang , L. Ding projective and Ding injective modules. To appear in Colloquium Algebra, available at:http://202.201.18.40:8080/mas5/labs/ home.jsp?id=135
   Google Scholar
• Communicated by I. Swanson.
   Google Scholar