Some results on the cofiniteness of local cohomology modules

Laleh, Sohrab Sohrabi, Sadeghi, Mir Yousef, and Mostaghim, Mahdi Hanifi. "Some results on the cofiniteness of local cohomology modules." Czechoslovak Mathematical Journal 62.1 (2012): 105-110. <http://eudml.org/doc/246139>.

@article{Laleh2012,
abstract = {Let $R$ be a commutative Noetherian ring, $\mathfrak \{a\}$ an ideal of $R$, $M$ an $R$-module and $t$ a non-negative integer. In this paper we show that the class of minimax modules includes the class of $\mathcal \{AF\}$ modules. The main result is that if the $R$-module $\{\rm Ext\}^t_R(R/\mathfrak \{a\},M)$ is finite (finitely generated), $H^i_\mathfrak \{a\}(M)$ is $\mathfrak \{a\} $-cofinite for all $i<t$ and $H^t_\mathfrak \{a\}(M)$ is minimax then $H^t_\mathfrak \{a\}(M)$ is $\mathfrak \{a\} $-cofinite. As a consequence we show that if $M$ and $N$ are finite $R$-modules and $H^i_\mathfrak \{a\}(N)$ is minimax for all $i<t$ then the set of associated prime ideals of the generalized local cohomology module $H^t_\mathfrak \{a\}(M,N)$ is finite.},
author = {Laleh, Sohrab Sohrabi, Sadeghi, Mir Yousef, Mostaghim, Mahdi Hanifi},
journal = {Czechoslovak Mathematical Journal},
keywords = {local cohomology; cofinite modules; mimimax modules; AF modules; associated primes; local cohomology; cofinite modules; minimax modules},
language = {eng},
number = {1},
pages = {105-110},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Some results on the cofiniteness of local cohomology modules},
url = {http://eudml.org/doc/246139},
volume = {62},
year = {2012},
}

TY - JOUR
AU - Laleh, Sohrab Sohrabi
AU - Sadeghi, Mir Yousef
AU - Mostaghim, Mahdi Hanifi
TI - Some results on the cofiniteness of local cohomology modules
JO - Czechoslovak Mathematical Journal
PY - 2012
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 62
IS - 1
SP - 105
EP - 110
AB - Let $R$ be a commutative Noetherian ring, $\mathfrak {a}$ an ideal of $R$, $M$ an $R$-module and $t$ a non-negative integer. In this paper we show that the class of minimax modules includes the class of $\mathcal {AF}$ modules. The main result is that if the $R$-module ${\rm Ext}^t_R(R/\mathfrak {a},M)$ is finite (finitely generated), $H^i_\mathfrak {a}(M)$ is $\mathfrak {a} $-cofinite for all $i<t$ and $H^t_\mathfrak {a}(M)$ is minimax then $H^t_\mathfrak {a}(M)$ is $\mathfrak {a} $-cofinite. As a consequence we show that if $M$ and $N$ are finite $R$-modules and $H^i_\mathfrak {a}(N)$ is minimax for all $i<t$ then the set of associated prime ideals of the generalized local cohomology module $H^t_\mathfrak {a}(M,N)$ is finite.
LA - eng
KW - local cohomology; cofinite modules; mimimax modules; AF modules; associated primes; local cohomology; cofinite modules; minimax modules
UR - http://eudml.org/doc/246139
ER -