… theorem that the category M (R, I)cof of I-cofinite modules over a commutative Noetherian
local ring R forms an Abelian subcategory of the category of all R-modules. Consequently, this …

… R-module M we define q ( I , M ) = M - cd ( I , M ) , where M denotes the Serre category of all
Artinian I-cofinite R-modules. … cohomology modules H I t ( M ) with t ∈ { q ( I , M ) , q ( I , M ) } . …

… , dim R/I = l), then the local cohomology modules H;(M) are I-cofinite; that is, Exti(R/Z,I$(M)) …
of P-cofinite modules form an abelian subcategory of the category of all R-modules. Finally, …

… category C ( R , I ) cof of I-cofinite modules is an Abelian subcategory of the category of
all R-modules… M → N is an R-homomorphism of I-cofinite modules, are ker f and coker f I-cofinite? …

… module [24]. We also show that if dimA = 1, then each a-cofinite module is a minimax module
… local ring and therefore the category of p-cofinite modules is an abelian subcategory of the …

… cofinite modules and one of the three modules Ker f, Im f and Coker f is a-cofinite, then all three
of them are a-cofinite. … we obtain that the category of a-cofinite artinian modules is abelian …

… As another application of Theorem 1.2, we prove that the category of the cofinite modules
with respect to an ideal generated by one element up to radical is an Abelian category (see …

… category of all a-weakly cofinite modules over R forms a full Abelian subcategory of the category
of modules… is to establish that the category of modules weakly cofinite with respect to an …

… But he used the derived category and showed that the … Since M is a j -cofinite we have that
M is a -cofinite module … Since M is an -cofinite module we have that H 0 (M) is an -cofinite for …

… of FD<n R-modules is a Serre subcategory of the category of R-… module of X is finite [15,
Definition 2.1]. Also, we say that X is an a-weakly cofinite R-module if X is an a-torsion R-module …