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Let $R\rightarrow S$ be a ring homomorphism. The relations of Gorenstein projective dimension with respect to a semidualizing module of homologically bounded complexes between $U\otimes_{R}^{\mathbf{L}}X$ and $X$ are considered, where $X$ is an $R$-complex and $U$ is an $S$-complex. Some sufficient conditions are given under which the equality $\mathcal{GP}_{\widetilde{C}}\text{-}\mathrm{pd}_{S}(S\otimes^{\mathbf{L}}_{R}X)=\mathcal{GP}_{C}\text{-}\mathrm{pd}_{R}(X)$ holds. As an application it is shown that the Auslander-Buchsbaum formula holds for $G_{C}$-projective dimension.
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참고문헌 (18)
참고문헌 신청
Luchezar L. Avramov / 1990 / Gorenstein local homomorphisms / Bulletin of the American Mathematical Society 23(1):145~150
LL Avramov / 1997 / Ring Homomorphisms and Finite Gorenstein Dimension / Proceedings of the London Mathematical Society 75(2):241~270
W. Bruns / 1993 / Cohen-Macaulay Rings / Cambridge University Press
Lars Winther Christensen / 2001 / Semi-dualizing complexes and their Auslander categories / Transactions of the American Mathematical Society 353(5):1839~1883
Lars Winther Christensen / 2009 / Ascent Properties of Auslander Categories / Canadian Journal of Mathematics 61(1):76~108
LL Avramov / 1997 / Ring Homomorphisms and Finite Gorenstein Dimension / Proceedings of the London Mathematical Society 75(2):241~270
W. Bruns / 1993 / Cohen-Macaulay Rings / Cambridge University Press
Lars Winther Christensen / 2001 / Semi-dualizing complexes and their Auslander categories / Transactions of the American Mathematical Society 353(5):1839~1883
Lars Winther Christensen / 2009 / Ascent Properties of Auslander Categories / Canadian Journal of Mathematics 61(1):76~108
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