arXiv subjects
Publications and source records attributed to M. Mast Zohouri.
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 $λ_{\mathfrak a}^{\mathfrak b}(M)$ of $M$, where the underlying module $M$ is relative Cohen-Macaulay w.r.t $\mathfrak a$. Some applications of such modules are given.
Let R be a commutative Noetherian ring, a a proper ideal of R and M a finite R-module. It is shown that, if (R;m) is a complete local ring, then under certain conditions a contains a regular element on DR(Hc a(M)), where c = cd(a;M). A non-zerodivisor characterization of relative Cohen-Macaulay modules w.r.t a is given. We introduce the concept of relative Cohen-Macaulay filtered modules w.r.t a and study some basic properties of such modules. In paticular, we provide a non-zerodivisor characterization of relative Cohen-Macaulay filtered modules w.r.t a. Furthermore, a characterization of cohomological dimension filtration of M by the associated prime ideals of its factors is established. As a consequence, we present a cohomological dimension filtration for those modules whose zero submodule has a primary decomposition. Finally, we bring some new results about relative Cohen- Macaulay modules w.r.t a.