A finiteness condition on regular local overrings of a local domain

Finiteness of certain local cohomology modules

Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ with respect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. Furthermore, Artinianness of $H^{j}_{mathfrak{b}_{0}}(H_{mathfrak{a}}^{i}(M,N))$ is investigated by using the above result, in certain graded situations, where $mathfrak{b}_{0}$ is an idea...

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

UPPER BOUNDS FOR FINITENESS OF GENERALIZED LOCAL COHOMOLOGY MODULES

Let $R$ be a commutative Noetherian ring with non-zero identity and $fa$ 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 $lc^{i}_{fa}(M,N)$ in certain Serre subcategories of the category of modules from upper bounds. We define and study the properti...

On the Finiteness of Local Homology Modules

Let (R,m) be a commutative Noetherian complete local ring, a an ideal of R, and A an Artinian R-module with N-dim A = d. We prove that if d > 0, then Cosupp(H d−1(A)) is finite and if d ≤ 3, then the set Coass(H i (A)) is finite for all i. Moreover, if either d ≤ 2 or the cohomological dimension cd(a) = 1 then H i (A) is a-coartinian for all i; that is, Torj (R/a,H a i (A)) is Artinian for all ...

Some Finiteness Conditions on the Set of Overrings of an Integral Domain