## Point sets containing their triangle centers

A vertex-transitive map $X$ is a map on a closed surface on which the automorphism group ${\rm Aut}(X)$ acts transitively on the set of vertices. If the face-cycles at all the vertices in a map are of same type then the map is said to be a semi-equivelar map. Clearly, a vertex-transitive map is semi-equivelar. Converse of this is not true in genera...

International audience

Published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We present a new and simpler proof of a combinatorial nature for the commutative case of Wood’s theorem which states that a finite ring has a generating character if and only if it is a Frobenius ring.

Published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We prove that Euler’s ratio-sum formula is valid in a projective-metric space if and only if it is either elliptic, hyperbolic, or Minkowskian.

Published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We use suitable maximum principles in order to obtain characterization results concerning n-dimensional linear Weingarten submanifolds immersed with globally flat normal bundle and parallel normalized mean curvature vector field in the (n+p)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{ams...

Published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

Betten and Riesinger (Aequ Math 81:227–250, 2011) constructed parallelisms of PG(3,R)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathrm{PG}(3,\mathbb {R})}$$\end{...

Published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

We generalize the notion of multi-Gieseker semistability for coherent sheaves, introduced by Greb, Ross, and Toma, to quiver sheaves for a quiver Q. We construct coarse moduli spaces for semistable quiver sheaves using a functorial method that realizes these as subschemes of moduli spaces of representations of a twisted quiver, depending on Q, with...

Let $\mathfrak{a}$ be an ideal in a commutative ring $R$. For an $R$-module $M$, we consider the small $\mathfrak{a}$-torsion $\Gamma_{\mathfrak{a}}(M)=\{x\in M\mid\exists n\in\mathbb{N}:\mathfrak{a}^n\subseteq(0:_Rx)\}$ and the large $\mathfrak{a}$-torsion $\overline{\Gamma}_{\mathfrak{a}}(M)=\{x\in M\mid\mathfrak{a}\subseteq\sqrt{(0:_Rx)}\}$. Thi...

Published in Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry

There are many homological dimensions which are closely related to ring theoretic properties. The notion of a AB ring has been introduced by Huneke and Jorgensen. It has nice homological properties. In this paper, we shall define a homological dimension which is closely related to a AB ring, and investigate its properties.