Related papers: Almost reverse lexicographic ideals and Fr\"{o}ber…

We use Macaulay's inverse system to study the Hilbert series for almost complete intersections generated by uniform powers of general linear forms. This allows us to give a classification of the Weak Lefschetz property for these algebras,…

We provide an irreducibility test in the ring K[[x]][y] whose complexity is quasi-linear with respect to the valuation of the discriminant, assuming the input polynomial F square-free and K a perfect field of characteristic zero or greater…

Let $(\mathcal{O}_n, \mathfrak{m})$ denote the ring of germs of holomorphic functions $\mathbb{C}^n\to \mathbb{C}$, and let $I\subseteq \mathcal{O}_n$ be an $\mathfrak{m}$-primary ideal. Demailly and Pham showed that $\mathrm{lct}(I) \geq…

In this paper we introduce the concepts of arbitrary $t$-spread lexsegments and of arbitrary $t$-spread lexsegment ideals with $t$ a positive integer. These concepts are a natural generalization of arbitrary lexsegments and arbitrary…

Over the years questions have arisen about T-ideals of (noncommutative) polynomials. But when evaluating a noncentral polynomial in subalgebras of matrices, one often has little control in determining the specific evaluations of the…

We study the rings of invariants for the indecomposable modular representations of the Klein four group. For each such representation we compute the Noether number and give minimal generating sets for the Hilbert ideal and the field of…

Let R be a commutative noetherian ring. Lindo and Pande have recently posed the question asking when every ideal of R is isomorphic to some trace ideal of R. This paper studies this question and gives several answers. In particular, a…

This paper mainly focuses on commutative local domains of dimension one. We then obtain a criterion for a ring to have a finite number of trace ideals in terms of integrally closed ideals. We also explore properties of such rings related to…

We give a criterion for a collection of polynomials to be a universal Gr\"{o}bner basis for an ideal in terms of the multidegree of the closure of the corresponding affine variety in $(\mathbb{P}^1)^N$. This criterion can be used to give…

This paper investigates the relation between the almost Gorenstein properties for graded rings and for local rings. Once $R$ is an almost Gorenstein graded ring, the localization $R_M$ of $R$ at the graded maximal ideal $M$ is almost…

In this paper we give an effective characterization of Hilbert functions and polynomials of standard algebras over an Artinian equicharacteristic local ring; the cohomological properties of such algebras are also studied. We describe…

We study modules over the Carlitz ring, a counterpart of the Weyl algebra in analysis over local fields of positive characteristic. It is shown that some basic objects of function field arithmetic, like the Carlitz module, Thakur's…

We study the normalization of a monomial ideal, and show how to compute its Hilbert function (using Ehrhart polynomials) if the ideal is zero dimensional. A positive lower bound for the second coefficient of the Hilbert polynomial is shown.

We study almost complete intersection ideals in a polynomial ring, generated by powers of all the variables together with a power of their sum. Our main result is an explicit description of the reduced Gr\"obner bases for these ideals under…

In this work, we provide a necessary and sufficient condition on a polyomino ideal for having the set of inner 2-minors as degree reverse lexicographic Gr\"obner basis, due to combinatorial properties of the polyomino itself. Moreover, we…

In this paper, we define on one hand, the notions of characteristics as well as central characteristics ideals of a given Leibniz algebra g and provide a necessary condition under which for two given subalgebras J and K of g such that, J IS…

In this article, we introduce and study the concept of $\phi$-2-absorbing quasi primary ideals in commutative rings. Let $R$ be a commutative ring with a nonzero identity and $L(R)$ be the lattice of all ideals of $R$. Suppose that…

Let $k[x]_{(x)}$ be the polynomial ring $k[x]$ localized in the maximal ideal $(x)\subseteq k[x]$. We study the Hilbert functor parameterizing ideals of colength $n$ in this ring {\it having support at the origin}. The main result of this…

We describe the ideals, especially the prime ideals, of semirings of polynomials over layered domains, and in particular over supertropical domains. Since there are so many of them, special attention is paid to the ideals arising from…

Let $(A,\m)$ be a Noetherian local ring with infinite residue field and let $I$ be an ideal in $A$ and let $F(I) = \oplus_{n \geq 0}I^n/\m I^n$ be the fiber-cone of $I$. We prove certain relations among the Hilbert coefficients of $F(I)$…