The finiteness dimension of modules and relative Cohen-Macaulayness

Abstract

Let $R$ be a commutative Noetherian ring, $\mathfrak{a}$ and $\mathfrak{b}$ ideals of $R$. In this paper, we study the finiteness dimension $f_{\mathfrak{a}}(M)$ of $M$ relative to $\mathfrak{a}$ and the $\mathfrak{b}$-minimum $\mathfrak{a}$-adjusted depth ${\lambda }_{\mathfrak{a}}^{\mathfrak{b}}(M)$ of $M$, where the underlying module $M$ is relative Cohen-Macaulay w.r.t $\mathfrak{a}$. Some applications of such modules are given.

References in corpus (2)

• On The Cohomological Dimension of Local Cohomology Modules
• Relative Cohen-Macaulay filtered modules with a view toward relative Cohen-Macaulay modules