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- W3115890484 abstract "Let $(R,mathfrak{m})$ is a $d$-dimensional Noetherian local ring and $T$ be a commutative strict algebra with unit element $1_T$ over $R$ such that $mathfrak{m}Tneq T$. We define almost exact sequences of $T$-modules and characterize almost flat $T$-modules. Moreover, we define almost (faithfully) flat homomorphisms between $R$-algebras $T$ and $W$, where $W$ has similar properties that $T$ has as an $R$-algebra. By almost (faithfully) flat homomorphisms and almost flat modules, we investigate Cousin complexes of $T$ and $W$-modules. Finally, for a finite filtration of length less than $d$ of $mathrm{Spec}(T)$, $mathcal{F}=(F_i)_{igeq0}$ such that admits a $T$-module $X$, we show that $^Imathrm{E}_{p,q}^2:=mathrm{Tor}_p^T left(M,mathrm{H}^{d-q}left(mathcal{C}_Tleft(mathcal{F},Xright)right)right) stackrel{p}{Rightarrow}mathrm{H}_{p+q}(mathrm{Tot}(mathcal{T}))$ and $^{II}mathrm{E}_{p,q}^2:=mathrm{H}^{d-p}left(mathrm{Tor}_q^Tleft(M,mathcal{C}_Tleft(mathcal{F},Xright)right)right) stackrel{p}{Rightarrow}mathrm{H}_{p+q}(mathrm{Tot}(mathcal{T}))$, where $M$ is an any flat $T$-module and as result we show that $^Imathrm{E}_{p,q}^2$ and $^{II}mathrm{E}_{p,q}^2$ are almost zero, when $M$ is almost flat." @default.
- W3115890484 created "2021-01-05" @default.
- W3115890484 creator A5041612711 @default.
- W3115890484 creator A5085017670 @default.
- W3115890484 date "2020-12-24" @default.
- W3115890484 modified "2023-10-09" @default.
- W3115890484 title "Cousin Complexes and almost flat rings" @default.
- W3115890484 doi "https://doi.org/10.30495/jme.v0i0.1504" @default.
- W3115890484 hasPublicationYear "2020" @default.
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