Let $R=\oplus_{n\in \Bbb N_0}R_n$ be a Noetherian homogeneous ring with local base ring $(R_0,\frak{m}_0)$, $M$ and $N$ two finitely generated graded $R$-modules. Let $t$ be the least integer such that $H^t_{R_+}(M,N)$ is not minimax. We prove that $H^j_{\frak{m}_0R}(H^t_{R_+}(M,N))$ is Artinian for $j=0,1$. Also, we show that if ${\rm cd}(R_{+},M,N)=2$ and $t\in \Bbb N_0$, then $H^t_{\frak{m}_0R}(H^2_{R_+}(M,N))$ is Artinian if and only if $H^{t+2}_{\frak{m}_0R}(H^1_{R_+}(M,N))$ is Artinian.
Gu, Y., & Chu, L. (2015). The Artinian property of certain graded generalized local chohomology modules. Bulletin of the Iranian Mathematical Society, 41(2), 423-428.
MLA
Gu, Y., & Chu, L. "The Artinian property of certain graded generalized local chohomology modules", Bulletin of the Iranian Mathematical Society, 41, 2, 2015, 423-428.
HARVARD
Gu Y., Chu L. (2015). 'The Artinian property of certain graded generalized local chohomology modules', Bulletin of the Iranian Mathematical Society, 41(2), pp. 423-428.
CHICAGO
Y. Gu & L. Chu, "The Artinian property of certain graded generalized local chohomology modules," Bulletin of the Iranian Mathematical Society, 41 2 (2015): 423-428,
VANCOUVER
Gu Y., Chu L. The Artinian property of certain graded generalized local chohomology modules. BIMS. 2015;41(2):423-428.
