Geodesic
Generalized tilting modules over ring extension
Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 801-810
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Let $ \Gamma $ be a ring extension of $R$. We show the left $\Gamma $-module $U=\Gamma \otimes _{R}C$ with the endmorphism ring End$_{\Gamma }U=\Delta $ is a generalized tilting module when $_{R}C$ is a generalized tilting module under some conditions.
Let $ \Gamma $ be a ring extension of $R$. We show the left $\Gamma $-module $U=\Gamma \otimes _{R}C$ with the endmorphism ring End$_{\Gamma }U=\Delta $ is a generalized tilting module when $_{R}C$ is a generalized tilting module under some conditions.
DOI : 10.21136/CMJ.2019.0512-17
Classification : 13D02, 13D05, 13D07
Keywords: ring extension; generalized tilting module; faithfully balanced bimodule 
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Zhang, Zhen. Generalized tilting modules over ring extension. Czechoslovak Mathematical Journal, Tome 69 (2019) no. 3, pp. 801-810. doi: 10.21136/CMJ.2019.0512-17

[1] Assem, I., Marmaridis, N.: Tilting modules over split-by-nilpotent extensions. Commun. Algebra 26 (1998), 1547-1555. | DOI | MR | JFM

[2] Christensen, L. W.: Semi-dualizing complexes and their Auslander categories. Trans. Am. Math. Soc. 353 (2001), 1839-1883. | DOI | MR | JFM

[3] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra. De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin (2000). | DOI | MR | JFM

[4] Foxby, H.-B.: Gorenstein modules and related modules. Math. Scand. 31 (1972), 267-284. | DOI | MR | JFM

[5] Fuller, K. R.: *-modules over ring extensions. Commun. Algebra 25 (1997), 2839-2860. | DOI | MR | JFM

[6] Fuller, K. R.: Ring extensions and duality. Algebra and Its Applications Contemp. Math. 259, American Mathematical Society, Providence D. V. Huynh et al. (2000), 213-222. | DOI | MR | JFM

[7] Göbel, R., Trlifaj, J.: Approximations and Endomorphism Algebras of Modules. De Gruyter Expositions in Mathematics 41, Walter De Gruyter, Berlin (2006). | DOI | MR | JFM

[8] Golod, E. S.: $G$-dimension and generalized perfect ideals. Tr. Mat. Inst. Steklova Russian 165 (1984), 62-66. | MR | JFM

[9] Holm, H., White, D.: Foxby equivalence over associative rings. J. Math. Kyoto Univ. 47 (2007), 781-808. | DOI | MR | JFM

[10] Miyashita, Y.: Tilting modules of finite projective dimension. Math. Z. 193 (1986), 113-146. | DOI | MR | JFM

[11] Sather-Wagstaff, S., Sharif, T., White, D.: Comparison of relative cohomology theories with respect to semidualizing modules. Math. Z. 264 (2010), 571-600. | DOI | MR | JFM

[12] Sather-Wagstaff, S., Sharif, T., White, D.: Tate cohomology with respect to semidualizing modules. J. Algebra 324 (2010), 2336-2368. | DOI | MR | JFM

[13] Sather-Wagstaff, S., Sharif, T., White, D.: AB-contexts and stability for Gorenstein flat modules with respect to semidualizing modules. Algebr. Represent. Theory 14 (2011), 403-428. | DOI | MR | JFM

[14] Tonolo, A.: $n$-cotilting and $n$-tilting modules over ring extensions. Forum Math. 17 (2005), 555-567. | DOI | MR | JFM

[15] Vasconcelos, W. V.: 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). | DOI | MR | JFM

[16] Wakamatsu, T.: On modules with trivial self-extensions. J. Algebra 114 (1988), 106-114. | DOI | MR | JFM

[17] Wakamatsu, T.: Stable equivalence for self-injective algebras and a generalization of tilting modules. J. Algebra 134 (1990), 298-325. | DOI | MR | JFM

[18] Wakamatsu, T.: Tilting modules and Auslander's Gorenstein property. J. Algebra 275 (2004), 3-39. | DOI | MR | JFM

[19] Wei, J.: $n$-star modules over ring extensions. J. Algebra 310 (2007), 903-916. | DOI | MR | JFM

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