Abstract
Let Γ be a ring extension of R. We show the left Γ-module U = Γ Ⓧr C with the endmorphism ring EndΓU = Δ is a generalized tilting module when RC is a generalized tilting module under some conditions.
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References
I. Assem, N. Marmaridis: Tilting modules over split-by-nilpotent extensions. Commun. Algebra 26 (1998), 1547–1555.
L. W. Christensen: Semi-dualizing complexes and their Auslander categories.. Trans. Am. Math. Soc. 353 (2001), 1839–1883.
E. E. Enochs, O. M. G. Jenda: Relative Homological Algebra. De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin, 2000.
H.-B. Foxby: Gorenstein modules and related modules. Math. Scand. 31 (1972), 267–284.
K. R. Fuller: *-modules over ring extensions. Commun. Algebra 25 (1997), 2839–2860.
K. R. Fuller: Ring extensions and duality. Algebra and Its Applications (D. V. Huynh et al., eds.). Contemp. Math. 259, American Mathematical Society, Providence, 2000, pp. 213–222.
R. Göbel, J. Trlifaj: Approximations and Endomorphism Algebras of Modules. De Gruyter Expositions in Mathematics 41, Walter De Gruyter, Berlin, 2006.
E. S. Golod: G-dimension and generalized perfect ideals. Tr. Mat. Inst. Steklova 165 (1984), 62–66. (In Russian.)
H. Holm, D. White: Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47 (2007), 781–808.
Y. Miyashita: Tilting modules of finite projective dimension. Math. Z. 193 (1986), 113–146.
S. Sather-Wagstaff, T. Sharif, D. White: Comparison of relative cohomology theories with respect to semidualizing modules. Math. Z. 264 (2010), 571–600.
S. Sather-Wagstaff, T. Sharif, D. White: Tate cohomology with respect to semidualizing modules. J. Algebra 324 (2010), 2336–2368.
S. Sather-Wagstaff, T. Sharif, D. White: AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules. Algebr. Represent. Theory 14 (2011), 403–428.
A. Tonolo: n-cotilting and n-tilting modules over ring extensions. Forum Math. 17 (2005), 555–567.
W. V. Vasconcelos: Divisor Theory in Module Categories. North-Holland Mathematics Studies 14. Notas de Matematica 53, North-Holland Publishing, Amsterdam; American Elsevier Publishing Company, New York, 1974.
T. Wakamatsu: On modules with trivial self-extensions. J. Algebra 114 (1988), 106–114.
T. Wakamatsu: Stable equivalence for self-injective algebras and a generalization of tilting modules. J. Algebra 134 (1990), 298–325.
T. Wakamatsu: Tilting modules and Auslander’s Gorenstein property. J. Algebra 275 (2004), 3–39.
J. Wei: n-star modules over ring extensions. J. Algebra 310 (2007), 903–916.
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The authors would like to express their sincere thanks to the referee for his or her careful reading of the manuscript and helpful suggestions.
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This research was partially supported by the ShanDong Provincial Natural Science Foundation of China (No. ZR2015PA001) and National Natural Science Foundation of China (No. 11371196).
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Zhang, Z. Generalized Tilting Modules Over Ring Extension. Czech Math J 69, 801–810 (2019). https://doi.org/10.21136/CMJ.2019.0512-17
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DOI: https://doi.org/10.21136/CMJ.2019.0512-17