Tate Cohomology for Complexes with Finite Gorenstein AC-Injective Dimension

Bulletin of the Iranian Mathematical Society - Tập 45 Số 1 - Trang 103-125 - 2019
Jun Xing1, Tiwei Zhao2, Yunxia Li3, Jiangsheng Hu4
1School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao, China
2School of Mathematical Sciences, Qufu Normal University, Qufu, China
3Department of Basic Science, Jinling Institute of Technology, Nanjing, China
4School of Mathematics and Physics, Jiangsu University of Technology, Changzhou, China

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Tài liệu tham khảo

Asadollahi, J., Salarian, S.: Cohomology theories based on Gorenstein injective modules. Trans. Am. Math. Soc. 358, 2183–2203 (2005)

Asadollahi, J., Salarian, S.: Gorenstein injective dimension for complexes and Iwanaga-Gorenstein rings. Commun. Algebra 34, 3009–3022 (2006)

Avramov, L.L., Foxby, H.-B.: Homological dimensions of unbounded complexes. J. Pure Appl. Algebra 71, 129–155 (1991)

Avramov, L.L., Martsinkovsky, A.: Absolute, relative, and Tate cohomology of modules of finite Gorenstein dimension. Proc. Lond. Math. Soc. 85, 393–440 (2002)

Bravo, D., Gillespie, J., Hovey, M.: The stable module category of a general ring, arXiv:1405.5768 (2014)

Cartan, H., Eilenberg, S.: Homological algebra. Princeton Univ. Press, Princeton (1956)

Christensen, L.W.: Gorenstein Dimension. Lecture Notes in Math, vol. 1747. Springer, Berlin (2000)

Christensen, L.W., Frankild, A., Holm, H.: On Gorenstein projective, injective and flat dimensions-a functorial description with applications. J. Algebra 302, 231–279 (2006)

Enochs, E.E., Jenda, O.M.G.: Gorenstein injective and projective modules. Math. Z. 220(4), 611–633 (1995)

Enochs, E.E., Jenda, O.M.G.: Relative homological algebra. Walter de Gruyter, Berlin (2000)

Gao, Z., Wang, F.: Weak injective and weak flat modules. Commun. Algebra 43, 3857–3868 (2015)

Gao, Z., Zhao, T.: Foxby equivalence relative to $$C$$ C -weak injective and $$C$$ C -weak flat modules. J. Korean Math. Soc. 54(5), 1457–1482 (2017)

Gillespie, J.: The flat model structure on Ch $$(R)$$ ( R ) . Trans. Am. Math. Soc. 356, 3369–3390 (2004)

Gillespie, J.: Model structures on modules over Ding-Chen rings. Homol. Homotopy Appl. 12(1), 61–73 (2010)

Holm, H.: Gorenstein homological dimensions. J. Pure Appl. Algebra 189, 167–193 (2004)

Holm, H.: Gorenstein derived functors. Proc. Am. Math. Soc. 132(7), 1913–1923 (2004)

Hovey, M.: Cotorsion pairs and model categories. Contemp. Math. 436, 277–296 (2007)

Hu, J., Ding, N.: A model structure approach to the Tate-Vogel cohomology. J. Pure Appl. Algebra 220(6), 2240–2264 (2016)

Iacob, A.: Generalized Tate cohomology. Tsukuba J. Math. 29, 389–404 (2005)

Megibben, C.: Absolutely pure modules. Proc. Am. Math. Soc. 26, 561–566 (1970)

Salce, L.: Cotorsion theories for abelian groups. Symposia Math. 23, 11–32 (1979)

Sather-Wagstaff, S., Sharif, T., White, D.: Tate cohomology with respect to semidualizing modules. J. Algeba 324, 2336–2368 (2010)

Spaltenstein, N.: Resolutions of unbounded complexes. Compositio Math. 65, 121–154 (1988)

Veliche, O.: Gorenstein projective dimension for complexes. Trans. Am. Math. Soc. 358, 1257–1283 (2006)

Wang, Z., Liu, Z.: Strongly Gorenstein flat dimensions of complexes. Commun. Algebra 44, 1390–1410 (2016)

Yang, G., Liu, Z.: Cotorsion pairs and model structures on Ch( $$R$$ R ). Proc. Edinb. Math. Soc. 54, 783–797 (2012)

Yang, X., Ding, N.: On a question of Gillespie. Forum Math. 27(6), 3205–3231 (2015)

Zhao, T., Xu, Y.: On right orthogonal classes and cohomology over Ding-Chen rings. Bull. Malays. Math. Sci. Soc. 40, 617–634 (2017)