A Note on Homological Dimensions of Artinian Local Cohomology Modules

Canadian mathematical bulletin

Kamal Bahmanpour¹ 

[1] Department of Mathematics, Ardabil branch Islamic Azad University, P.O. Box 5614633167, Ardabil, Iran

关键词: cofinite modules;    flat dimension;    injective dimension;    Krull dimension;    local cohomology;   

DOI  :  10.4153/CMB-2011-197-9

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $(R,{frak m})$ be a non-zero commutative Noetherian local ring(with identity), $M$ be a non-zero finitely generated $R$-module. Inthis paper for any ${frak p}in {m Spec}(R)$ we show that $ operatorname{{m injdim_{_{R_{frak p}}}}}H^{i-dim(R/{frak p})}_{{frak p}R_{frak p}}(M_{frak p})$ and ${m fd}_{R_{p}} H^{i-dim(R/{frak p})}_{{frak p}R_{frakp}}(M_{frak p})$ are bounded from above by $operatorname{{m injdim_{_{R}}}} H^i_{frak m}(M)$ and $ {m fd}_R H^i_{frak m}(M)$ respectively, for all integers $igeq dim(R/{frak p})$.

【 授权许可】

Unknown