Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0710.1019

Generic fiber of power series ring extensions

Tiberiu Dumitrescu
View original source ↗Read source document ↗Export metadata ↓

Abstract

Let D be a Noetherian domain containing a field, d a nonzero nonunit of D and z an indeterminate over D. We prove that the generic fiber of D[1/d][[z]] over D[[z]] has dimension greater than the dimension of D/dD.

Explore related subjects

math.ACmath.AG

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Tiberiu Dumitrescu. 2007-10-09. Generic fiber of power series ring extensions. https://arxiv.org/abs/0710.1019

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Co-Hopfian Modules

If $R$ is a commutative ring with $1$, then a co-Hopfian $R$-module $M$ is necessarily a module of fractions over a ring of fractions. For $R$ commutative Noetherian, we use Matlis' notion of modules with maximal orders together with localization to obtain results about co-Hopfian submodules of indecomposable injectives and co-Hopfian finitely generated P-primary $R$-modules. With suitable restriction, we determine co-Hopfian and Hopfian submodules of a co-Hopfian injective module.

math.AC↗
arXiv2026

$t$-Young complexes and squarefree powers of $t$-path ideals

We introduce a new class of simplicial complexes, called \emph{$t$-Young complexes}, arising from Young diagrams and a positive integer~$t$. We show that every $t$-Young complex is either contractible or homotopy equivalent to a wedge of spheres, and a complete characterization of their vertex-decomposability is provided. Interestingly, $t$-Young complexes naturally appear as the Alexander dual complexes of squarefree powers of $t$-path ideals of path graphs. For this family, we use generating functions to obtain an explicit formula for homotopy type. As applications, we determine the projective dimension and the Krull dimension of these squarefree powers.

math.AC↗
arXiv2026

Characterization of Some Graphs Realizing Regularity Bounds for Binomial Edge Ideals

In this paper, we characterize all graphs $G$ satisfying \[\operatorname{reg}(S/J_G)=\ell(G)=c(G)\] where $\ell(G)$ is the sum of the lengths of the longest induced paths in each connected component of $G$ and $c(G)$ is the number of the maximal cliques of $G$. We also characterize all connected graphs $G$ that satisfy \[\operatorname{reg}(S/J_G)=\ell(G)=|V(G)|-ω(G)+1\] where $ω(G)$ is the clique number of $G$. Moreover, we investigate the possible values of the regularity of $S/J_G$ within the intervals $[\ell(G), c(G)]$ and $[\ell(G), |V(G)|-ω(G)+1]$.

math.AC↗