Related papers: Normally torsion-free lexsegment ideals

We introduce the class of principal symmetric ideals, which are ideals generated by the orbit of a single polynomial under the action of the symmetric group. Fixing the degree of the generating polynomial, this class of ideals is…

In this article we prove that every toric ideal associated with a gap-free graph $G$ has a squarefree lexicographic initial ideal. Moreover, in the particular case when the complementary graph of $G$ is chordal (i.e. when the edge ideal of…

We prove that level binomial edge ideals with regularity 2 and pseudo-Gorenstein binomial edge ideals with regularity 3 are cones, and we describe them completely. Also, we characterize level and pseudo-Gorenstein binomial edge ideals of…

We study the licci property for several classes of squarefree monomial ideals arising from graphs and related combinatorial structures. We characterize licci bi-Cohen-Macaulay squarefree monomial ideals, complementary edge ideals, $t$-path…

We prove that each positive power of the maximal ideal of a commutative Noetherian local ring is Tor-rigid, and strongly-rigid. This gives new characterizations of regularity and, in particular, shows that such ideals satisfy the torsion…

The objective of this article is to give an effective algebraic characterization of normal crossing hypersurfaces in complex manifolds. It is shown that a hypersurface has normal crossings if and only if it is a free divisor, has a radical…

Let $C^*(E)$ be the graph C$^*$-algebra of a row-finite graph $E$. We give a complete description of the vertex sets of the gauge-invariant regular ideals of $C^*(E)$. It is shown that when $E$ satisfies Condition (L) the regular ideals…

The classical notion of {\L}ojasiewicz ideals of smooth functions is studied in the context of non-quasianalytic Denjoy-Carleman classes. In the case of principal ideals, we obtain a characterization of {\L}ojasiewicz ideals in terms of…

In this paper, we discuss the normality of the toric rings of stable set polytopes, and the set of generators and Gr\"obner bases of toric ideals of stable set polytopes by using the results on that of edge polytopes of finite nonsimple…

We show that the class of completely m-full ideals coincides with the class of componentwise linear ideals in a polynomial ring over an infinite field.

We construct finitely generated torsion-free solvable groups $G$ that have infinite rank, but such that all finitely generated torsion-free metabelian subquotients of $G$ are virtually abelian. In particular all finitely generated…

To define the notion of a generic property of finite dimensional 2-step nilpotent Lie algebras we use standard correspondence between such Lie algebras and points of an appropriate algebraic variety, where a negligible set is one contained…

For two ideals $I$ and $J$ of a noetherian ring, we characterize, in terms of the vanishing of Tor modules, when the associated graded ring of the sum $I+J$ is isomorphic to the tensor product of the associated graded ring of $I$ and the…

Using the division polynomials for elliptic curves in Weierstrass form, it shown that the group of rational points on the curve $H: ky(yy - 1) = lx(xx - 1)$ is torsion-free.

In this article, we shall characterize torsionfreeness of modules with respect to a semidualizing module in terms of the Serre's condition (S_n). As its applications, we give a characterization of Cohen-Macaulay rings R such that R_p is…

In this paper, we consider certain topological properties along with certain types of mappings on these spaces defined by the notion of ideal convergence. In order to do that, we primarily follow in the footsteps of the earlier studies of…

Every normal toric ideal of codimension two is minimally generated by a Grobner basis with squarefree initial monomials. A polynomial time algorithm is presented for checking whether a toric ideal of fixed codimension is normal.

While one can in principle augment gravity theory with torsion, it is generally thought that any such torsion affects would be too small to be of consequence. Here we show that this cannot in general be the case. We show that the limit of…

Starting from context-free inverse graphs, we introduce a new class of groups and study their structural properties. We establish closure properties, show that their co-word problems are context-free, analyze torsion elements, and realize…

Let $S$ be a polynomial ring over a field and $I\subseteq S$ a homogeneous ideal containing a regular sequence of forms of degrees $d_1, \ldots, d_c$. In this paper we prove the Lex-plus-powers Conjecture when the field has characteristic 0…