Gorenstein homological dimensions with respect to a semidualizing module
In this paper, let R be a commutative ring and C a semidualizing
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- D. Bennis and N. Mahdou, Strongly Gorenstein projective, injective, and
flat modules, J. Pure Appl. Algebra, 210(2) (2007), 437-445.
- D. Bennis and N. Mahdou, Global Gorenstein dimensions, Proc. Amer. Math.
Soc., 138(2) (2010), 461-465.
- I. Emmanouil, On the niteness of Gorenstein homological dimensions, J. Al-
gebra, 372 (2012), 376-396.
- E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, De Gruyter
Expositions in Mathematics, 3, Walter de Gruyter & Co., Berlin, 2000.
- R. M. Fossum, P. A. Grith and I. Reiten, Trivial Extensions of Abelian Cate-
gories, Homological algebra of trivial extensions of abelian categories with ap-
plications to ring theory, Lecture Notes in Mathematics, 456, Springer-Verlag,
Berlin-New York, 1975.
- H.-B. Foxby, Gorenstein modules and related modules, Math. Scand., 31 (1972),
267-284.
- E. S. Golod, G-dimension and generalized perfect ideals, Trudy Mat. Inst.
Steklov., 165 (1984), 62-66.
- H. Holm, Gorenstein homological dimensions, J. Pure Appl. Algebra, 189(1-3)
(2004), 167-193.
- H. Holm and P. Jrgensen, Semi-dualizing modules and related Gorenstein
homological dimensions, J. Pure Appl. Algebra, 205(2) (2006), 423-445.
- H. Holm and D. White, Foxby equivalence over associative rings, J. Math.
Kyoto Univ., 47(4) (2007), 781-808.
- S. Sather-Wagstaff, T. Sharif and D. White, Tate cohomology with respect to
semidualizing modules, J. Algebra, 324(9) (2010), 2336-2368.
- W. V. Vasconcelos, Divisor Theory in Module Categories, North-Holland
Mathematics Studies, 14, North-Holland Publishing Co., Amsterdam-Oxford;
American Elsevier Publishing Co., Inc., New York, 1974.
- C. A. Weibel, An Introduction to Homological Algebra, Cambridge Stud. Adv.
Math., 38, Cambridge University Press, Cambridge, 1994.
- D. White, Gorenstein projective dimension with respect to a semidualizing mod-
ule, J. Commut. Algebra, 2(1) (2010), 111-137.
- G. Zhao and J. Sun, Global dimensions of rings with respect to a semidualizing
module, avilable from https://arxiv.org/abs/1307.0628.