Mathematics – Commutative Algebra
Scientific paper
2011-01-23
Mathematics
Commutative Algebra
18pages, with some revisions and corrections
Scientific paper
Let $R=\bigoplus_{n\geq 0}R_n$, $\fa\supseteq \bigoplus_{n> 0}R_n$ and $M$ and $N$ be a standard graded ring, an ideal of $R$ and two finitely generated graded $R$-modules, respectively. This paper studies the homogeneous components of graded generalized local cohomology modules. First of all, we show that for all $i\geq 0$, $H^i_{\fa}(M, N)_n$, the $n$-th graded component of the $i$-th generalized local cohomology module of $M$ and $N$ with respect to $\fa$, vanishes for all $n\gg 0$. Furthermore, some sufficient conditions are proposed to satisfy the equality $\sup\{\en(H^i_{\fa}(M, N))| i\geq 0\}= \sup\{\en(H^i_{R_+}(M, N))| i\geq 0\}$. Some sufficient conditions are also proposed for tameness of $H^i_{\fa}(M, N)$ such that $i= f_{\fa}^{R_+}(M, N)$ or $i= \cd_{\fa}(M, N)$, where $f_{\fa}^{R_+}(M, N)$ and $\cd_{\fa}(M, N)$ denote the $R_+$-finiteness dimension and the cohomological dimension of $M$ and $N$ with respect to $\fa$, respectively. We finally consider the Artinian property of some submodules and quotient modules of $H^j_{\fa}(M, N)$, where $j$ is the first or last non-minimax level of $H^i_{\fa}(M, N)$.
Jahangiri Maryam
Shirmohammadi N.
Tahamtan Sh.
No associations
LandOfFree
Tameness and Artinianness of Graded Generalized Local Cohomology Modules does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Tameness and Artinianness of Graded Generalized Local Cohomology Modules, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Tameness and Artinianness of Graded Generalized Local Cohomology Modules will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-587027