Left-Derived Functors of the Generalized <i>I</i>-Adic Completion and Generalized Local Homology

Nam, Tran Tuan

doi:10.1080/00927870802578043

Cited by 8 publications

(6 citation statements)

References 15 publications

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“…Then {X, ϕ i : X → X i } i is the inverse limit of the inverse system {X i , ϕ ij : X j → X i } i≤j (see [13,Chapter 2] for more details about the inverse system and inverse limit). This inverse limit is called n-th generalized local homology of M, N with respect to a and is denoted by H a n (M, N ); see [2,3,10,11] for more details and basic properties. Now, we show that the R-module X also has an R a -module structure, where…”

Section: R) These Inclusions Yield the Equation (24)mentioning

confidence: 99%

On the finiteness of local homology modules

Fathi¹,

Hajikarimi²

2021

Preprint

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Let R be a commutative Noetherian ring and a an ideal of R. Let M be a finitely generated R-module and N an Artinian R-module. The concept of filter coregular sequence is introduced to determine the infimum of the integers i such that the generalized local homology H a i (M, N ) is not finitely generated as an R a -module, where R a denotes the a-adic completion of R. In particular, it is shown that H a i (M, N ) is a finitely generated R a -module for all i ∈ N 0 if and only if (0 : N a + Ann R (M )) has finite length whenever R is a complete semi-local ring.

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Section: R) These Inclusions Yield the Equation (24)mentioning

confidence: 99%

On the finiteness of local homology modules

Fathi¹,

Hajikarimi²

2021

Preprint

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“…• is a flat resolution of M and N an arbitrary R-module. In [23] T. Nam introduced the notion of the generalized completion homology modules L i Λ I (N, M), for i ∈ Z, as the homologies of the complex lim…”

Section: Introductionmentioning

confidence: 99%

On generalized completion homology modules

Mahmood¹

2015

Preprint

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“…This definition of generalised local homology modules is in some sense dual to the definition of generalised local cohomology modules of Herzog [5] and in fact a generalisation of the usual local homology H I i (M) = lim ← − −t Tor R i (R/I t , M). In [10] we also studied some basic properties of the left derived functor and showed that if M is a finitely generated R-module and N a linearly compact R-module, then…”

Section: Introductionmentioning

confidence: 99%