Related papers: Normally torsion-free lexsegment ideals

The stratum St(J,<) (the homogeneous stratum Sth(J,<) respectively) of a monomial ideal J in a polynomial ring R is the family of all (homogeneous) ideals of R whose initial ideal with respect to the term order < is J. St(J,<) and Sth(J,<)…

We say that an ideal I is homogeneous, if its restriction to any I-positive subset is isomorphic to I. The paper investigates basic properties of this notion -- we give examples of homogeneous ideals and present some applications to…

We prove the existence of infinite dense free sets (in the usual topology) for set mappings on the reals, under reasonable assumptions.

Let A be a commutative noetherian ring, and \a an ideal in it. In this paper we continue the study, begun in [PSY1], of the derived \a-adic completion and the derived \a-torsion functors. Here are our results: (1) a structural…

We give an explicit construction of a maximal torsion-free finite-index subgroup of a certain type of Coxeter group. The subgroup is constructed as the fundamental group of a finite and non-positively curved polygonal complex. First we…

We study the torsion of the $\alpha$-connections defined on the density manifold in terms of a regular Riemannian metric. In the case of the Fisher-Rao metric our results confirm the fact that all $\alpha$-connections are torsion free. For…

In this paper we discuss some affine properties of convex equal-area polygons, which are convex polygons such that all triangles formed by three consecutive vertices have the same area. Besides being able to approximate closed convex smooth…

The Jacobian ideal provides the set of infinitesimally trivial deformations for a homogeneous polynomial, or for the corresponding complex projective hypersurface. In this article, we investigate whether the associated linear deformation is…

A curve $\gamma$ in a Riemannian manifold $M$ is three-dimensional if its torsion (signed second curvature function) is well-defined and all higher-order curvatures vanish identically. In particular, when $\gamma$ lies on an oriented…

The notion of ideal immersions was introduced by the author in 1990s. Roughly speaking, an ideal immersion of a Riemannian manifold into a real space form is a nice isometric immersion which produces the least possible amount of tension…

In this paper we prove that, for any $n\in \mathbb N$, the ideal generated by $n$ slice regular functions $f_1,\ldots,f_n$ having no common zeros concides with the entire ring of slice regular functions. The proof required the study of the…

We provide detailed local descriptions of stable polynomials in terms of their homogeneous decompositions, Puiseux expansions, and transfer function realizations. We use this theory to first prove that bounded rational functions on the…

The $k$-secant degree is studied with a combinatorial approach. A planar toric degeneration of any projective toric surface $X$ corresponds to a regular unimodular triangulation $D$ of the polytope defining $X$. If the secant ideal of the…

We study torsion torsionfree(=TTF) triples in abelian and triangulated categories. (Notice that TTF triples in a triangulated category are essentially in bijection with recollement data for this triangulated category.) In particular, we…

The central question of this paper is: how do algebraic invariants of edge ideals change under natural graph operations? We study this question through the lens of suspensions. The (full) suspension of a graph is obtained by adjoining a new…

Let $\Omega \subset \mathbb{R}^n$ be a convex domain and let $f:\Omega \rightarrow \mathbb{R}$ be a subharmonic function, $\Delta f \geq 0$, which satisfies $f \geq 0$ on the boundary $\partial \Omega$. Then $$ \int_{\Omega}{f ~dx} \leq…

We show that the zero locus of a normal function on a smooth complex algebraic variety S is algebraic provided that the normal function extends to a admissible normal function on a smooth compactification of S with torsion singularity. This…

We show that a torsion-free nilpotent loop (that is, a loop nilpotent with respect to the dimension filtration) has a torsion-free nilpotent left multiplication group of, at most, the same class. We also prove that a free loop is residually…

For a set $X\subseteq \mathbb{N}$, we define the $X$-torsion of a group $G$ to be all elements $g\in G$ with $g^{n}=e$ for some $n\in X$. With $X$ recursively enumerable, we give two independent proofs (group-theoretic, and model-theoretic)…

In this study, we present the generalization of the concept of $r$-ideals in commutative rings with nonzero identity. Let $R$ be a commutative ring with $0\neq1$ and $L(R)$ be the lattice of all ideals of $R$. Suppose that…