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Title: Generalized tilting modules over ring extension (English)
Author: Zhang, Zhen
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 69
Issue: 3
Year: 2019
Pages: 801-810
Summary lang: English
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Category: math
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Summary: 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. (English)
Keyword: ring extension
Keyword: generalized tilting module
Keyword: faithfully balanced bimodule
MSC: 13D02
MSC: 13D05
MSC: 13D07
idZBL: Zbl 07088817
idMR: MR3989279
DOI: 10.21136/CMJ.2019.0512-17
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Date available: 2019-07-24T11:19:27Z
Last updated: 2021-10-04
Stable URL: http://hdl.handle.net/10338.dmlcz/147790
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Reference: [1] Assem, I., Marmaridis, N.: Tilting modules over split-by-nilpotent extensions.Commun. Algebra 26 (1998), 1547-1555. Zbl 0915.16007, MR 1622428, 10.1080/00927879808826219
Reference: [2] Christensen, L. W.: Semi-dualizing complexes and their Auslander categories..Trans. Am. Math. Soc. 353 (2001), 1839-1883. Zbl 0969.13006, MR 1813596, 10.1090/S0002-9947-01-02627-7
Reference: [3] Enochs, E. E., Jenda, O. M. G.: Relative Homological Algebra.De Gruyter Expositions in Mathematics 30, Walter de Gruyter, Berlin (2000). Zbl 0952.13001, MR 1753146, 10.1515/9783110803662
Reference: [4] Foxby, H.-B.: Gorenstein modules and related modules.Math. Scand. 31 (1972), 267-284. Zbl 0272.13009, MR 0327752, 10.7146/math.scand.a-11434
Reference: [5] Fuller, K. R.: *-modules over ring extensions.Commun. Algebra 25 (1997), 2839-2860. Zbl 0885.16019, MR 1458733, 10.1080/00927879708826026
Reference: [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. Zbl 0965.16004, MR 1778503, 10.1090/conm/259
Reference: [7] Göbel, R., Trlifaj, J.: Approximations and Endomorphism Algebras of Modules.De Gruyter Expositions in Mathematics 41, Walter De Gruyter, Berlin (2006). Zbl 1121.16002, MR 2251271, 10.1090/conm/259
Reference: [8] Golod, E. S.: $G$-dimension and generalized perfect ideals.Tr. Mat. Inst. Steklova Russian 165 (1984), 62-66. Zbl 0577.13008, MR 0752933
Reference: [9] Holm, H., White, D.: Foxby equivalence over associative rings.J. Math. Kyoto Univ. 47 (2007), 781-808. Zbl 1154.16007, MR 2413065, 10.1215/kjm/1250692289
Reference: [10] Miyashita, Y.: Tilting modules of finite projective dimension.Math. Z. 193 (1986), 113-146. Zbl 0578.16015, MR 0852914, 10.1007/BF01163359
Reference: [11] Sather-Wagstaff, S., Sharif, T., White, D.: Comparison of relative cohomology theories with respect to semidualizing modules.Math. Z. 264 (2010), 571-600. Zbl 1190.13007, MR 2591820, 10.1007/s00209-009-0480-4
Reference: [12] Sather-Wagstaff, S., Sharif, T., White, D.: Tate cohomology with respect to semidualizing modules.J. Algebra 324 (2010), 2336-2368. Zbl 1207.13009, MR 2684143, 10.1016/j.jalgebra.2010.07.007
Reference: [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. Zbl 1317.13029, MR 2785915, 10.1007/s10468-009-9195-9
Reference: [14] Tonolo, A.: $n$-cotilting and $n$-tilting modules over ring extensions.Forum Math. 17 (2005), 555-567. Zbl 1088.16011, MR 2154419, 10.1515/form.2005.17.4.555
Reference: [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). Zbl 0296.13005, MR 0498530, 10.1016/s0304-0208(08)x7021-5
Reference: [16] Wakamatsu, T.: On modules with trivial self-extensions.J. Algebra 114 (1988), 106-114. Zbl 0646.16025, MR 0931903, 10.1016/0021-8693(88)90215-3
Reference: [17] Wakamatsu, T.: Stable equivalence for self-injective algebras and a generalization of tilting modules.J. Algebra 134 (1990), 298-325. Zbl 0726.16009, MR 1074331, 10.1016/0021-8693(90)90055-S
Reference: [18] Wakamatsu, T.: Tilting modules and Auslander's Gorenstein property.J. Algebra 275 (2004), 3-39. Zbl 1076.16006, MR 2047438, 10.1016/j.jalgebra.2003.12.008
Reference: [19] Wei, J.: $n$-star modules over ring extensions.J. Algebra 310 (2007), 903-916. Zbl 1118.16011, MR 2308185, 10.1016/j.jalgebra.2006.10.026
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