1. CMB Online first
 Bavula, V. V.; Lu, T.

Classification of simple weight modules over the SchrÃ¶dinger algebra
A classification of simple weight modules over the SchrÃ¶dinger
algebra is given. The Krull and the global dimensions are found
for the centralizer $C_{\mathcal{S}}(H)$ (and some of its prime factor
algebras) of the Cartan element $H$ in the universal enveloping
algebra $\mathcal{S}$ of the SchrÃ¶dinger (Lie) algebra. The simple
$C_{\mathcal{S}}(H)$modules are classified. The Krull and the global
dimensions are found for some (prime) factor algebras of the
algebra $\mathcal{S}$ (over the centre). It is proved that some (prime)
factor algebras of $\mathcal{S}$ and $C_{\mathcal{S}}(H)$ are tensor homological/Krull
minimal.
Keywords:weight module, simple module, centralizer, Krull dimension, global dimension, tensor homological minimal algebra, tensor Krull minimal algebra Categories:17B10, 17B20, 17B35, 16E10, 16P90, 16P40, 16P50 

2. CMB 2012 (vol 56 pp. 491)
 Bahmanpour, Kamal

A Note on Homological Dimensions of Artinian Local Cohomology Modules
Let $(R,{\frak m})$ be a nonzero commutative Noetherian local ring
(with identity), $M$ be a nonzero finitely generated $R$module. In
this paper for any ${\frak p}\in {\rm Spec}(R)$ we show that
$
\operatorname{{\rm injdim_{_{R_{\frak p}}}}}
H^{i\dim(R/{\frak p})}_{{\frak p}R_{\frak p}}(M_{\frak p})$ and
${\rm fd}_{R_{\p}} H^{i\dim(R/{\frak p})}_{{\frak p}R_{\frak
p}}(M_{\frak p})$ are bounded from above by $
\operatorname{{\rm injdim_{_{R}}}}
H^i_{\frak
m}(M)$ and
$ {\rm fd}_R H^i_{\frak m}(M)$ respectively, for all integers $i\geq \dim(R/{\frak p})$.
Keywords:cofinite modules, flat dimension, injective dimension, Krull dimension, local cohomology Category:13D45 
