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Let $\mathcal{W}$ be an additive full subcategory of the category $R$-Mod of left $R$-modules. We provide a method to construct a proper $\mathcal{W}_C^H$-resolution (resp. coproper $\mathcal{W}_C^T$-coresolution) of one term in a short exact sequence in $R$-Mod from those of the other two terms. By using these constructions, we introduce and study the stability of the Gorenstein categories $\mathcal{G}_C(\mathcal{WW}_C^T)$ and $\mathcal{G}_C(\mathcal{W}_C^H\mathcal{W})$ with respect to a semidualizing bimodule $C$, and investigate the 2-out-of-3 property of these categories of a short exact sequence by using these constructions. Also we prove how they are related to the Gorenstein categories $\mathcal{G}((R\ltimes C)\otimes_R\mathcal{W})_C$ and $\mathcal{G}(\textrm{Hom}_R(R\ltimes C,\mathcal{W}))_C$ over $R\ltimes C$.
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참고문헌 (12)
참고문헌 신청
M. Auslander / 1969 / Stable Module Theory / Mem. Amer. Math. Soc 94
L. W. Christensen / 2000 / Gorenstein dimensions, Lecture Notes in Math. vol. 1747 / Springer
E. E. Enochs / 1995 / Gorenstein injective and projective modules / Math. Z 220(4):611~633
E. E. Enochs / 2005 / Covers and envelopes by V -Gorenstein modules / Comm. Algebra 33(12):4705~4717
H.-B. Foxby / 1972 / Gorenstein modules and related modules / Math. Scand 31:267~284
L. W. Christensen / 2000 / Gorenstein dimensions, Lecture Notes in Math. vol. 1747 / Springer
E. E. Enochs / 1995 / Gorenstein injective and projective modules / Math. Z 220(4):611~633
E. E. Enochs / 2005 / Covers and envelopes by V -Gorenstein modules / Comm. Algebra 33(12):4705~4717
H.-B. Foxby / 1972 / Gorenstein modules and related modules / Math. Scand 31:267~284
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