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TRANSFER PROPERTIES OF GORENSTEIN HOMOLOGICAL DIMENSION WITH RESPECT TO A SEMIDUALIZING MODULE
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 Title & Authors
TRANSFER PROPERTIES OF GORENSTEIN HOMOLOGICAL DIMENSION WITH RESPECT TO A SEMIDUALIZING MODULE
Di, Zhenxing; Yang, Xiaoyan;
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 Abstract
The classes of homological modules over commutative ring, where C is a semidualizing module, extend Holm and Jgensen's notions of C-Gorenstein homological modules to the non-Noetherian setting and generalize the classical classes of homological modules and the classes of Gorenstein homological modules within this setting. On the other hand, transfer of homological properties along ring homomorphisms is already a classical field of study. Motivated by the ideas mentioned above, in this article we will investigate the transfer properties of C and homological dimension.
 Keywords
semidualizing module;ring homomorphism;C homological modules; homological modules;localization;
 Language
English
 Cited by
1.
BALANCE FOR RELATIVE HOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES,;;;

대한수학회보, 2015. vol.52. 1, pp.137-147 crossref(new window)
1.
BALANCE FOR RELATIVE HOMOLOGY WITH RESPECT TO SEMIDUALIZING MODULES, Bulletin of the Korean Mathematical Society, 2015, 52, 1, 137  crossref(new windwow)
 References
1.
L. L. Avramov and H. B. Foxby, Homological dimensions of unbounded complexes, J. Pure Appl. Algebra. 71 (1991), no. 2-3, 129-155. crossref(new window)

2.
L. W. Christensen, Gorenstein Dimensions, Lecture Notes in Mathematics, vol. 1747, Springer-Verlag, Berlin, 2000.

3.
L. W. Christensen and H. Holm, Ascent properties of Auslander categories, Canad. J. Math. 61 (2009), no. 13, 76-108. crossref(new window)

4.
E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, Walter de Gruyter, New York, Spring-Verlag, 2000.

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, Gorenstein homological dimensions, J. Pure Appl. Algebra. 189 (2004), no. 1-3, 167-193. crossref(new window)

8.
H. Holm and P. Jgensen, Semi-dualizing modules and related Gorenstein homological dimensions, J. Pure Appl. Algebra. 205 (2006), no. 2, 423-445. crossref(new window)

9.
H. Holm and D. White, Foxby equivalence over associative rings, J. Math. Kyoto Univ. 47 (2007), no. 4, 781-808.

10.
T. Y. Lam, Lecture on Modules and Rings, Springer-Verlag, New York, 1999.

11.
M. S. Osborne, Basic Homological Algebra, Graduate Texts in Mathematics, 196. Springer-Verlag, New York, 2000.

12.
J. J. Rotman, An Introduction to Homological Algebra, Academic Press, New York, 1979.

13.
W. V. Vasconcelos, Divisor Theory in Module Categories, North-Holland Publishing Co., Amsterdam, 1974

14.
X. Y. Yang and Z. K. Liu, Strongly Gorenstein projective, injective and at modules, J. Algebra. 320 (2008), no. 7, 2659-2674. crossref(new window)

15.
D. White, Gorenstein projective dimension with respect to a semidualizing module, J. Commut. Algebra 2 (2010), no. 1, 111-137. crossref(new window)