arXiv subjects

Negar Alipour

Publications and source records attributed to Negar Alipour.

2 recordsLinked to original sources

arXiv2022

Cofiniteness with respect to extension of Serre subcategories

Let $R$ be a commutative noetherian ring, $\frak a$ be an ideal of $R$, $\mathcal{S}$ be an arbitrary Serre subcategory of $R$-modules satisfying the condition $C_{\frak a}$ and let $\mathcal{N}$ be the subcategory of finitely generated $R$-modules. In this paper, we define and study $\mathcal{NS}$-$\frak a$-cofinite modules with respect to the extension subcategory $\mathcal{NS}$ as an generalization of the classical notion, namely $\frak a$-cofinite modules. For the lower dimensions, we show that the classical results of $\frak a$-cofiniteness hold for the new notion.

math.AC↗

arXiv2020

A new dimension for Grothendieck categories via the atom spectrum

In this paper, we define a new dimension for objects in a Grothendieck category $\mathcal{A}$. We show that it serves as a lower bound for Gabriel-Krull dimension and under certain conditions, the two dimensions coincide. We carry out our investigation for a fully right bounded ring $A$. We introduce a new spectrum Comp$\,A$ via compressible right $A$-modules. In analogy with dimension theory for commutative rings, we show that the Krull dimension of right $A$-modules can be computed via the length of chain of prime ideals of $A$ and also the length of chain of elements of Comp$\,A$.

math.CT↗