ARTINIANNESS OF COMPOSED LOCAL COHOMOLOGY MODULES

Document Type : Original Manuscript

Author

Department of Mathematics, Sanandaj Branch, University Islamic Azad University, Sanandaj, Iran.

Abstract

Let

R

be a commutative Noetherian ring and let

f a

f b

be two ideals of

R

such that

R / (f a + f b)

is Artinian. Let

M

N

be two finitely generated

R

-modules. We prove that

H_{f b}^{j} (H_{f a}^{t} (M, N))

is Artinian for

j = 0, 1

, where

t = i n f i i n m a t h b b N_{0} : H_{f a}^{i} (M, N) $ i s n o t f i n i t e l y g e n e r a t e d $

. Also, we prove that if

D i m S u p p (H_{f a}^{i} (M, N)) l e q 2

, then

H_{f b}^{1} (H_{f a}^{i} (M, N))

is Artinian for all

i

. Moreover, we show that if

d i m N = d

, then

H_{f b}^{j} (H_{f a}^{d - 1} (N))

is Artinian for all

j g e q 1

Keywords