TY  - JOUR
T1  - Serre subcategory, generalized local homology and generalized local cohomology modules
AU  - Hatamkhani, Marziyeh
PY  - 2025
DA  - July
Y2  - 2025
DO  - 10.24330/ieja.1640842
JF  - International Electronic Journal of Algebra
JO  - IEJA
PB  - Abdullah HARMANCI
WT  - DergiPark
SN  - 1306-6048
SP  - 228
EP  - 242
VL  - 38
IS  - 38
LA  - en
AB  - This paper deals with generalized local homology and generalized local cohomology modules belong to a Serre category of the category of $R$-modules under some conditions. For an ideal $I$ of $R$, the concept of the condition $C^I$ on a Serre category  which is dual to the condition $C_I$ of Melkersson is defined. As a main result, it is shown that for a finitely generated $R$-module $M$ with $pd(M) <\infty$ and  a minimax $R$-module $N$ of any Serre category  $\mathcal{S}$ satisfying the condition $C^I$, the generalized local homology $\text{H}^I_i(M,N)$ belongs to $\mathcal{S}$ for all $i>pd(M)$. Also, if $\mathcal{S}$ satisfies the condition $C_I$, then the generalized local cohomology module   $\text{H}^i_I(M,N)\in \mathcal{S}$ for all $i>pd(M)$.
KW  - Generalized local homology module
KW  - generalized local cohomology module
KW  - Serre subcategory
KW  - minimax module
KW  - condition C^I
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UR  - https://doi.org/10.24330/ieja.1640842
L1  - https://dergipark.org.tr/en/download/article-file/4614083
ER  -