Transfer properties of Gorenstein homological dimension with respect to a semidualizing module
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초록
The classes of GC homological modules over commutative ring, where C is a semidualizing module, extend Holm and J gensen's notions of C-Gorenstein homological modules to the non-Noetherian set-ting 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 eld of study. Motivated by the ideas mentioned above, in this article we will investigate the transfer properties of C and GC homological dimension.
Abstract
The classes of GC homological modules over commutative ring, where C is a semidualizing module, extend Holm and J gensen's notions of C-Gorenstein homological modules to the non-Noetherian set-ting 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 eld of study. Motivated by the ideas mentioned above, in this article we will investigate the transfer properties of C and GC homological dimension.
참고문헌 (15)
- L. L. Avramov, "Homological dimensions of unbounded complexes", J. Pure Appl. Algebra, 71(2), pp.129~155 (1991)
- L. W. Christensen, "Gorenstein Dimensions, Lecture Notes in Mathematics, vol. 1747" (2000), Springer-Verlag
- L. W. Christensen, "Ascent properties of Auslander categories", Canad. J. Math, 61(13), pp.76~108 (2009)
- E. E. Enochs, "Relative Homological Algebra, Walter de Gruyter" (2000), Spring-Verlag
- H. B. Foxby, "Gorenstein modules and related modules", Math. Scand, 31, pp.267~284 (1972)
- E. S. Golod, "G-dimension and generalized perfect ideals", Trudy Mat. Inst. Steklov, 165, pp.62~66 (1984)
- H. Holm, "Gorenstein homological dimensions", J. Pure Appl. Algebra, 189(1), pp.167~193 (2004)
- H. Holm, "Semi-dualizing modules and related Gorenstein homological dimensions", J. Pure Appl. Algebra, 205(2), pp.423~445 (2006)
- H. Holm, "Foxby equivalence over associative rings", J. Math. Kyoto Univ, 47(4), pp.781~808 (2007)
- T. Y. Lam, "Lecture on Modules and Rings" (1999), Springer-Verlag
- M. S. Osborne, "Basic Homological Algebra, Graduate Texts in Mathematics" (2000), Springer-Verlag
- J. J. Rotman, "An Introduction to Homological Algebra" (1979), Academic Press
- W. V. Vasconcelos, "Divisor Theory in Module Categories" (1974), North-Holland Publishing Co
- X. Y. Yang, "Strongly Gorenstein projective, injective and at modules", J. Algebra, 320(7), pp.2659~2674 (2008)
- D. White, "Gorenstein projective dimension with respect to a semidualizing module", J. Commut. Algebra, 2(1), pp.111~137 (2010)