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𝓦-RESOLUTIONS AND GORENSTEIN CATEGORIES WITH RESPECT TO A SEMIDUALIZING BIMODULES
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 Title & Authors
𝓦-RESOLUTIONS AND GORENSTEIN CATEGORIES WITH RESPECT TO A SEMIDUALIZING BIMODULES
YANG, XIAOYAN;
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 Abstract
Let be an additive full subcategory of the category R-Mod of left R-modules. We provide a method to construct a proper -resolution (resp. coproper -coresolution) of one term in a short exact sequence in R-Mod from those of the other two terms. By using these constructions, we introduce and study the stability of the Gorenstein categories and with respect to a semidualizing bimodule C, and investigate the 2-out-of-3 property of these categories of a short exact sequence by using these constructions. Also we prove how they are related to the Gorenstein categories and over .
 Keywords
-resolution and -coresolution;Gorenstein category;
 Language
English
 Cited by
 References
1.
M. Auslander and M. Bridger, Stable Module Theory, Mem. Amer. Math. Soc. vol. 94, 1969.

2.
L. W. Christensen, Gorenstein dimensions, Lecture Notes in Math. vol. 1747, Springer, Berlin, 2000.

3.
E. E. Enochs and O. M. G. Jenda, Gorenstein injective and projective modules, Math. Z. 220 (1995), no. 4, 611-633. crossref(new window)

4.
E. E. Enochs, O. M. G. Jenda, and J. A. Lopez-Ramos, Covers and envelopes by V - Gorenstein modules, Comm. Algebra 33 (2005), no. 12, 4705-4717. crossref(new window)

5.
H.-B. Foxby, Gorenstein modules and related modules, Math. Scand. 31 (1972), 267-284.

6.
E. S. Golod, G-dimension and generalized perfect ideals, Trudy Mat. Inst. Steklov. 165 (1984), 62-66.

7.
H. Holm and P. Jorgensen, Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra 205 (2006), no. 2, 423-445. crossref(new window)

8.
H. Holm and D. White, Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (2007), no. 4, 781-808.

9.
Z. Y. Huang, Proper resolutions and Gorenstein categories, J. Algebra 393 (2013), 142-169. crossref(new window)

10.
S. Sather-Wagstaff, T. Sharif, and D. White, Stability of Gorenstein categories, J. Lon- don Math. Soc. 77 (2008), no. 2, 481-502.

11.
S. Sather-Wagstaff, AB-contexts and stability for Gorenstein flat modules with respect ro semidu- alizing modules, Algebr. Represent. Theory 14 (2011), no. 3, 403-428. crossref(new window)

12.
W. V. Vasconcelos, Divisor Theory in Module Categories, North-Holland Publishing Co., Amsterdam, 1974.