Abstract
Gorenstein injective modules and dimensions have been studied extensively by many authors. In this paper, we investigate Gorenstein injective modules and dimensions relative to a Wakamatsu tilting module.
Similar content being viewed by others
References
Anderson F W, Fuller K R. Rings and Categories of Modules. New York: Springer-Verlag, 1974
Bass H. Injective dimension in Noetherian rings. Trans Amer Math Soc, 1962, 102: 18–29
Beligiannis A, Reiten I. Homological and Homotopical Aspects of Torsion Theories. Mem Amer Math Soc, 188. Providence, RI: Amer Math Soc, 2007
Colby R R, Fuller K R. Equivalence and Duality for Module Categories (with Tilting and Cotilting for Rings); Cam-bridge Tracts in Mathematics 161. Cambridge: Cambridge University Press, 2004
Enochs E E. Injective and flat covers, envelopes and resolvents. Israel J Math, 1981, 39: 189–209
Enochs E E, Jenda O M G. Gorenstein injective and projective modules. Math Z, 1995, 220: 611–633
Enochs E E, Jenda O M G. Relative Homological Algebra. Berlin-New York: Walter de Gruyter, 2000
Enochs E E, Jenda O M G. On D-Gorenstein modules, Interactions between Ring Theory and Representatives of Algebras. New York: Marcel Dekker, 2000, 159–168
Enochs E E, Jenda O M G. Ω-Gorenstein projective and flat covers and Ω-Gorenstein injective envelopes. Comm Algebra, 2004, 32: 1453–1470
Enochs E E, Jenda O M G. Gorenstein and Ω-Gorenstein injective covers and flat preenvelopes. Comm Algebra, 2005, 33: 507–518
Enochs E E, Jenda O M G, López-Ramos J A. Covers and envelopes by V -Gorenstein modules. Comm Algebra, 2005, 33: 4705–4717
Hoshino M. Algebra of finite self-injective dimension. Proc Amer Math Soc, 1991, 112: 619–622
Holm H. Gorenstein homological dimensions. J Pure Appl Algebra, 2004, 189: 167–193
Huang Z Y, Tang G H. Self-orthogonal modules over coherent rings. J Pure Appl Algebra, 2001, 161: 167–176
Huang Z Y. Generalized tilting modules with finite injective dimension. J Algebra, 2007, 311: 619–634
Miyachi J. Duality for derived categories and cotilting bimodules. J Algebra, 1996, 185: 583–603
Nauman S K. Static modules and stable Clifford theory. J Algebra, 1990, 128: 497–509
Rotman J J. An Introduction to Homological Algebra. New York: Academic Press, 1979
Stenström B. Coherent rings and FP-injective modules. J London Math Soc, 1970, 2: 323–329
Wakamatsu T. Tilting modules and Auslander’s Gorenstein property. J Algebra, 2004, 275: 3–39
Wisbauer R. Static modules and equivalences. Lecture Notes in Pure and Appl. Math. 210. New York: CRC Press, 2000
Xu J, Cheng F. Homological dimensions over non-commutative semi-local rings. J Algebra, 1994, 169: 679–685
Xu J. Flat Covers of Modules; Lecture Notes in Math. 1634. Berlin-Heidelberg-New York: Springer-Verlag, 1996
Zhu H Y, Ding N Q. Wakamatsu tilting modules with finite FP-injective dimension. Forum Math, 2009, 21: 101–116
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Zhu, H., Ding, N. ω-Gorenstein injective modules and dimensions. Sci. China Math. 54, 421–436 (2011). https://doi.org/10.1007/s11425-010-4128-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11425-010-4128-y
Keywords
- Wakamatsu tilting module
- ω-Gorenstein injective module
- ω-Gorenstein injective dimension
- cotilting module