arXiv subjects

Mehdi Dorreh

Publications and source records attributed to Mehdi Dorreh.

4 recordsLinked to original sources

arXiv2017

On the injective dimension of F-finite modules and holonomic D-modules

Let $R$ be a regular local ring containing a field $k$ of characteristic $p$ and $M$ be an $\mathscr{F}$-finite module. In this paper, we study the injective dimension of $M$. We prove that $\operatorname{dim}_R(M) -1 \leq\operatorname{inj.dim}_R(M)$. If $R = k[[x_1,\ldots,x_n]]$ where $k$ is a field of characteristic $0$ we prove the analogous result for a class of holonomic $\mathscr{D}$-modules which contains local cohomology modules.

math.AC↗

arXiv2014

Direct summands of infinite-dimensional polynomial rings

Let k be a field and R a pure subring of the infinite-dimensional polynomial ring k[X1;...]. If R is generated by monomials, then we show that the equality of height and grade holds for all ideals of R. Also, we show R satisfies the weak Bourbaki unmixed property. As an application, we give the Cohen-Macaulay property of the invariant ring of the action of a linearly reductive group acting by k-automorphism on k[X1;...]. This provides several examples of non-Noetherian Cohen-Macaulay rings (e.g. Veronese, determinantal and Grassmanian rings).

math.AC↗

arXiv2013

Direct limits of Cohen-Macaulay rings

Let $A$ be a direct limit of a direct system of Cohen-Macaulay rings. In this paper, we describe the Cohen-Macaulay property of $A$. Our results indicate that $A$ is not necessarily Cohen-Macaulay. We show $A$ is Cohen-Macaulay under various assumptions. As an application, we study Cohen-Macaulayness of non-affine normal semigroup rings.

math.AC↗

arXiv2013

Cohen-Macaulayness of non-affine normal semigroups

In this paper, we study the Cohen-Macaulayness of non-affine normal semigroups in $\mathbb{Z}^n$. We do this by establishing the following four statements each of independent interest: 1) a Lazard type result on $I$-supported elements of $\prod_{\mathbb{N}}\mathbb{Q}_{\geq0}$ for an index set $I\subset\mathbb{N}$; 2) a criterion of regularity of sequences of elements of the ring via projective dimension; 3) a direct limit of polynomial rings with toric maps; 4) any direct summand of rings of the third item is Cohen-Macaulay. To illustrate the idea, we give many examples.

math.AC↗