%0 Journal Article %T A new lower bound for cohomological dimension %J Algebraic Structures and Their Applications %I Yazd University %Z 2382-9761 %A Nazari, Alireza %A Farokhi, Asghar %D 2020 %\ 02/01/2020 %V 7 %N 1 %P 21-28 %! A new lower bound for cohomological dimension %K cofinite modules %K cohomological dimension %K Local cohomology %R 10.22034/as.2020.1621 %X Let $(R,\mathfrak{m})$ be a Noetherian local ring, $M$ a finitely generated $R$-module, and $\mathfrak{a}$ an ideal of $R$. We define the $\mathfrak{a}$-minimum dimension $d(\mathfrak{a},M)$ of $M$ by $$d(\mathfrak{a},M)=Min\{\dim \frac{R}{\mathfrak{p}+\mathfrak{a}}:\mathfrak{p}\in Assh_{R}(M)\}.$$ In this paper, we show that $cd(\mathfrak{a},M)\geq \dim M-d(\mathfrak{a},M)$ and we give some sufficient conditions and characterization for the equality to hold true. %U https://as.yazd.ac.ir/article_1621_42a77c099b9affb629ee988bbd224dbb.pdf