On the Associated Primes of Generalized Local Cohomology Modules
نویسندگان
چکیده
منابع مشابه
On the Associated Primes of the generalized $d$-Local Cohomology Modules
The first part of the paper is concerned to relationship between the sets of associated primes of the generalized $d$-local cohomology modules and the ordinary generalized local cohomology modules. Assume that $R$ is a commutative Noetherian local ring, $M$ and $N$ are finitely generated $R$-modules and $d, t$ are two integers. We prove that $Ass H^t_d(M,N)=bigcup_{Iin Phi} Ass H^t_I(M,N)...
متن کاملOn the associated primes of generalized local cohomology modules
In [8], Huneke conjectured that if M is a finitely generated R-module, then the set of associated primes of H i a (M) is finite. Singh [15] provides a counter example for this conjecture. However, it is known that the conjecture is true in many situations. For example, in [11] it is shown that if R is local and dimR/a = 1, then for a finitely generated R-module M , the set AssR(H i a (M)) is fi...
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where the map R/(x1 , . . . , x m n ) −→ R/(x m+1 1 , . . . , x m+1 n ) is multiplication by the image of the element x1 · · ·xn. As these descriptions suggest, H a(R) is usually not finitely generated as an R-module. However local cohomology modules have useful finiteness properties in certain cases, e.g., for a local ring (R,m), the modules H m(R) satisfy the descending chain condition. This ...
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Let $M$ and $N$ be two finitely generated graded modules over a standard graded Noetherian ring $R=bigoplus_{ngeq 0} R_n$. In this paper we show that if $R_{0}$ is semi-local of dimension $leq 2$ then, the set $hbox{Ass}_{R_{0}}Big(H^{i}_{R_{+}}(M,N)_{n}Big)$ is asymptotically stable for $nrightarrow -infty$ in some special cases. Also, we study the torsion-freeness of graded generalized local ...
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ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2006
ISSN: 0092-7872,1532-4125
DOI: 10.1080/00927870600650739