Let $R$ be a commutative Noetherian ring with non-zero identity and $a$ an ideal of $R$. Let $M$ be a finite $R$--module of finite projective dimension and $N$ an arbitrary finite $R$--module. We characterize the membership of the generalized local cohomology modules $H^{i}_{a}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properties of a generalization of cohomological dimension of generalized local cohomology modules. Let $\mathcal S$ be a Serre subcategory of the category of $R$--modules and $n > pd M$ be an integer such that $H^{i}_{a}(M,N)$ belongs to $\mathcal S$ for all $i> n$. Then, for any ideal $b\supseteq a$, it is also shown that the module $H^{n}_{a}(M,N)/{b}H^{n}_{a}(M,N)$ belongs to $\mathcal S$.
Aghapournahr, M. (2013). UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES. Journal of Algebraic Systems, 1(1), 1-9. doi: 10.22044/jas.2013.169
MLA
Moharram Aghapournahr. "UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES", Journal of Algebraic Systems, 1, 1, 2013, 1-9. doi: 10.22044/jas.2013.169
HARVARD
Aghapournahr, M. (2013). 'UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES', Journal of Algebraic Systems, 1(1), pp. 1-9. doi: 10.22044/jas.2013.169
VANCOUVER
Aghapournahr, M. UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES. Journal of Algebraic Systems, 2013; 1(1): 1-9. doi: 10.22044/jas.2013.169
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