Add to ORKGLocal cohomology modules have played an important role in commutative algebra. These modules are usually not finitely generated; however, they have finiteness properties over local regular rings of equal characteristic. Namely, the associated primes and the Bass numbers of local cohomology modules are finite in this case. This work shows these properties for certain non-local regular rings, flat extensions with regular fibers, rings of mixed characteristic and direct summands. In addition, the F-Jacobian ideal, the generalized Lyubeznik numbers and the Lyubeznik numbers in mixed characteristic are defined by using finiteness properties of local cohomology. Furthermore, it is shown that these invariants relate to singularities of rings.PhDMa...
In this thesis we investigate when the set of primes of a local cohomology module is finite. We show...
Let R be a Noetherian ring, I an ideal of R, and M a finitely generated R-module. The i-th local coh...
In this thesis we investigate when the set of primes of a local cohomology module is finite. We show...
Local cohomology modules are one of the central objects in commutative algebra. However, the structu...
AbstractIf R is a commutative Noetherian regular ring containing a field and I is an ideal of R, it ...
In this paper, we show that for an F-pure local ring (R,m), all local cohomology modules Him(R) have...
Let $R$ be a noetherian ring, $\mathfrak a$ an ideal of $R$ such that $\dim R/{\mathfrak a}=1$ and $...
Let R be an excellent regular ring of dimension d containing a field K of characteristic zero. Let I...
AbstractLet a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We...
AbstractWe study, by using the theory of algebraic D-modules, the local cohomology modules supported...
summary:Let $R$ be a commutative Noetherian ring and ${\mathfrak a}$ an ideal of $R$. We introduce t...
Let (R, ) denote a commutative Noetherian local ring and let M be a finite R-module. In this paper, ...
We assume that all rings are commutative and noetherian with identity throughout this paper. 1
AbstractIn this note I give a description of Lyubeznik's local cohomology invariants for a certain n...
AbstractIn this paper, we present a condition on a local Cohen–Macaulay F-injective ring of positive...
In this thesis we investigate when the set of primes of a local cohomology module is finite. We show...
Let R be a Noetherian ring, I an ideal of R, and M a finitely generated R-module. The i-th local coh...
In this thesis we investigate when the set of primes of a local cohomology module is finite. We show...
Local cohomology modules are one of the central objects in commutative algebra. However, the structu...
AbstractIf R is a commutative Noetherian regular ring containing a field and I is an ideal of R, it ...
In this paper, we show that for an F-pure local ring (R,m), all local cohomology modules Him(R) have...
Let $R$ be a noetherian ring, $\mathfrak a$ an ideal of $R$ such that $\dim R/{\mathfrak a}=1$ and $...
Let R be an excellent regular ring of dimension d containing a field K of characteristic zero. Let I...
AbstractLet a be an ideal of a commutative Noetherian ring R and M a finitely generated R-module. We...
AbstractWe study, by using the theory of algebraic D-modules, the local cohomology modules supported...
summary:Let $R$ be a commutative Noetherian ring and ${\mathfrak a}$ an ideal of $R$. We introduce t...
Let (R, ) denote a commutative Noetherian local ring and let M be a finite R-module. In this paper, ...
We assume that all rings are commutative and noetherian with identity throughout this paper. 1
AbstractIn this note I give a description of Lyubeznik's local cohomology invariants for a certain n...
AbstractIn this paper, we present a condition on a local Cohen–Macaulay F-injective ring of positive...
In this thesis we investigate when the set of primes of a local cohomology module is finite. We show...
Let R be a Noetherian ring, I an ideal of R, and M a finitely generated R-module. The i-th local coh...
In this thesis we investigate when the set of primes of a local cohomology module is finite. We show...