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- W4301786937 abstract "Let $R$ be a commutative Noetherian ring, $fa$ an ideal of $R$ and $mathcal{D}(R)$ denote the derived category of $R$-modules. We investigate the theory of local homology in conjunction with Gorenstein flat modules. Let $X$ be a homologically bounded to the right complex and $Q$ a bounded to the right complex of Gorenstein flat $R$-modules such that $Q$ and $X$ are isomorphic in $mathcal{D}(R)$. We establish a natural isomorphism ${bf L}Lambda^{fa}(X)simeq Lambda^{fa}(Q)$ in $mathcal{D}(R)$ which immediately asserts that $sup {bf L}Lambda^{fa}(X)leq Gfd_RX$. This isomorphism yields several consequences. For instance, in the case $R$ possesses a dualizing complex, we show that $Gfd_R {bf L}Lambda^{fa}(X)leq Gfd_RX$. Also, we establish a criterion for regularity of Gorenstein local rings." @default.
- W4301786937 created "2022-10-05" @default.
- W4301786937 creator A5068835267 @default.
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- W4301786937 date "2012-01-15" @default.
- W4301786937 modified "2023-10-14" @default.
- W4301786937 title "Local homology and Gorenstein flat modules" @default.
- W4301786937 doi "https://doi.org/10.48550/arxiv.1201.3067" @default.
- W4301786937 hasPublicationYear "2012" @default.
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