Relative FP-injective and FP-flat complexes and their model structures

References

• Beligiannis, A., Reiten, I. (2007). Homological and homotopical aspects of torsion theories. Memoir Am Math Soc. 188(883): viii+207.
   Web of Science ®Google Scholar
• Bican, L., El Bashir, R., Enochs, E. (2001). All modules have flat covers. Bull. London Math. Soc. 33(4):385–390.
   Web of Science ®Google Scholar
• Bourbaki, N. (1989). Commutative Algebra. Chapters 1–7. Elements of Mathematics (Berlin). Berlin, Germany: Springer-Verlag. Translated from the French, Reprint of the 1972 edition.
   Google Scholar
• Bravo, D., Gillespie, J. (2016). Absolutely clean, level, and Gorenstein AC-injective complexes. Comm. Algebra. 44(5):2213–2233.
   Web of Science ®Google Scholar
• Bravo, D., Gillespie, J., Hovey, M. (2014). The Stable Module Category of a General Ring https://arxiv.org/abs/1405.5768.
   Google Scholar
• Bravo, D., Pérez, M. A. (2017). Finiteness conditions and cotorsion pairs. J. Pure Appl. Algebra. 221(6):1249–1267.
   Web of Science ®Google Scholar
• Chen, J., Ding, N. (1996). On n-coherent rings. Comm. Algebra. 24(10):3211–3216.
   Web of Science ®Google Scholar
• Cortés Izurdiaga, M., Estrada, S., Guil Asensio, P. A. (2012). A model structure approach to the finitistic dimension conjectures. Math. Nachr. 285(7):821–833.
   Web of Science ®Google Scholar
• Costa, D. L. (1994). Parameterizing families of non-Noetherian rings. Comm. Algebra. 22(10):3997–4011.
   Web of Science ®Google Scholar
• Dugger, D., Shipley, B. (2004). K-Theory and derived equivalences. Duke Math. J. 124(3):587–617.
   Google Scholar
• Eklof, P. C., Trlifaj, J. (2001). How to make Ext vanish. Bull. London Math. Soc. 33(1):41–51.
   Web of Science ®Google Scholar
• Enochs, E. E. (1981). Injective and flat covers, envelopes and resolvents. Israel J. Math. 39(3):189–209.
   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., Garcı́a Rozas, J. R. (1998). Flat covers of complexes. J. Algebra. 210(1):86–102.
   Web of Science ®Google Scholar
• Enochs, E. E., Jenda, O. M. G. (2000). Relative Homological Algebra, Volume 30 of De Gruyter Expositions in Mathematics. Berlin, Germany: Walter de Gruyter & Co.
   Google Scholar
• Enochs, E. E., Jenda, O. M. G. (2011). Relative Homological Algebra. Volume 2, Volume 54 of De Gruyter Expositions in Mathematics. Berlin, Germany: Walter de Gruyter GmbH & Co. KG.
   Google Scholar
• Enochs, E. E., López-Ramos, J. A. (2002). Kaplansky classes. Rend. Sem. Mat. Univ. Padova. 107:67–79.
   Google Scholar
• Fieldhouse, D. J. (1971). Character modules. Comment. Math. Helv. 46(1):274–276.
   Google Scholar
• Fieldhouse, D. J. (1972). Character modules, dimension and purity. Glasgow Math. J. 13(02):144–146.
   Google Scholar
• First, U. A. (2015). Rings that are Morita equivalent to their opposites. J. Algebra. 430:26–61.
   Web of Science ®Google Scholar
• Gao, Z., Huang, Z. (2016). Weak injective and weak flat complexes. Glasgow Math. J. 58(03):539–557.
   Google Scholar
• García Rozas, J. R. (1999). Covers and Envelopes in the Category of Complexes of Modules, Volume 407 of Chapman & Hall/CRC Research Notes in Mathematics. Boca Raton, FL: Chapman & Hall/CRC.
   Google Scholar
• Gillespie, J. (2004). The flat model structure on Ch(R). Trans. Amer. Math. Soc. 356(08):3369–3390.
   Google Scholar
• Gillespie, J. (2008). Cotorsion pairs and degreewise homological model structures. Homology Homotopy Appl. 10(1):283–304.
   Google Scholar
• Gillespie, J. (2017). Models for homotopy categories of injectives and Gorenstein injectives. Comm. Algebra. 45(6):2520–2545.
   Web of Science ®Google Scholar
• Glaz, S. (1989). Commutative Coherent Rings, Volume 1371 of Lecture Notes in Mathematics. Berlin, Germany: Springer-Verlag.
   Google Scholar
• Göbel, R., Trlifaj, J. (2006). Approximations and Endomorphism Algebras of Modules, Volume 41 of De Gruyter Expositions in Mathematics. Berlin, Germany: Walter de Gruyter GmbH & Co. KG.
   Google Scholar
• Holm, H., Jørgensen, P. (2009). Cotorsion pairs induced by duality pairs. J. Commut. Algebra. 1(4):621–633.
   Web of Science ®Google Scholar
• Hovey, M. (1999). Model Categories, Volume 63 of Mathematical Surveys and Monographs. Providence, RI: American Mathematical Society.
   Google Scholar
• Hovey, M. (2002). Cotorsion pairs, model category structures, and representation theory. Math. Z. 241(3):553–592.
   Web of Science ®Google Scholar
• Jacobson, N. (1985). Basic Algebra. I, 2nd ed. New York, NY: W. H. Freeman and Company.
   Google Scholar
• Pérez, M. A. (2016). Homological dimensions and abelian model structures on chain complexes. Rocky Mountain J. Math. 46(3):951–1010.
   Web of Science ®Google Scholar
• Pérez, M. A. (2016). Introduction to Abelian Model Structures and Gorenstein Homological Dimensions. Boca Raton, FL: CRC Press.
   Google Scholar
• Rotman, J. J. (2009). An Introduction to Homological Algebra. Universitext, 2nd ed. New York, NY: Springer.
   Google Scholar
• Stenström, B. (1975). Rings of Quotients: An Introduction to Methods of Ring Theory. New York, NY: Springer-Verlag. Die Grundlehren der Mathematischen Wissenschaften, Band 217.
   Google Scholar
• Wang, Z., Liu, Z. (2011). FP-injective complexes and FP-injective dimension of complexes. J. Aust. Math. Soc. 91(02):163–187.
   Google Scholar
• Yang, X. (2012). Cotorsion pairs of complexes. In Proceedings of the International Conference on Algebra 2010. Hackensack, NJ: World Sci. Publ, pp. 697–703.
   Google Scholar