Related papers: Weighted Veronese Rings via Convex Semigroups
Our goal is to convince the readers that the theory of complex normal surface singularities can be a powerful tool in the study of numerical semigroups, and, in the same time, a very rich source of interesting affine and numerical…
The integral group rings $\mathbb{Z}G$ for finite groups $G$ are precisely those fusion rings whose basis elements have Frobenius-Perron dimension 1, and each is categorifiable in the sense that it arises as the Grothendieck ring of a…
In this paper we develop a novel approach to Witt vector rings and to the (relative) de Rham Witt complex. We do this in the generality of arbitrary commutative algebras and arbitrary truncation sets. In our construction of Witt vector…
We present various facts on the graded Betti table of a projectively embedded toric surface, expressed in terms of the combinatorics of its defining lattice polygon. These facts include explicit formulas for a number of entries, as well as…
We introduce $\hat{H}$-eigenvalue for $2m$-th order $n$-dimensional complex tensors. Then we determine several checkable inclusion sets for $\hat{H}$-eigenvalues and derive some criterions for the Hermitian positive definiteness…
In this article, we consider the structure of graded rings, not necessarily commutative nor with unity, and study the graded weakly prime ideals. We investigate the graded rings in which all graded ideals are graded weakly prime. Several…
We give a criterion for almost Gorenstein property for semigroup rings associated with simplicial semigroups. We extend Nari's theorem for almost symmetric numerical semigroups to simplicial semigroups with higher rank. By this criterion,…
Motivated by properties of higher tangent lifts of geometric structures, we introduce concepts of weighted structures for various geometric objects on a manifold F equipped with a homogeneity structure. The latter is a smooth action on F of…
We investigate Rees algebras and special fiber rings obtained by blowing up specialized Ferrers ideals. This class of monomial ideals includes strongly stable monomial ideals generated in degree two and edge ideals of prominent classes of…
Kleshchev, Mathas and Ram (2012) gave a presentation for graded Specht modules over Khovanov-Lauda-Rouquier algebras of finite and affine type A. We show that this construction can be applied more generally to skew shapes to give a…
We define the $m$th Veronese power of a weight graded operad $\mathcal{P}$ to be its suboperad $\mathcal{P}^{[m]}$ generated by operations of weight $m$. It turns out that, unlike Veronese powers of associative algebras, homological…
We study inequalities between graded Betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps, defined earlier by us in [Math. Z. 274, (2013), no. 3-4, pp. 809-819; arXiv:1009.4488]. We show…
We study affine semigroup rings as algebras over subsemigroup rings. From this relative viewpoint with respect to a given subsemigroup ring, the fibered sum of two affine semigroup algebras is constructed. Such a construction is compared to…
In this article, we study the componentwise linear ideals in the Veronese subrings of $R=K[x_1,\ldots,x_n]$. If char$(K)=0$, then we give a characterization for graded ideals in the $c^{th}$ Veronese ring $R^{(c)}$ to be componentwise…
Matrix-valued holomorphic quantum modular forms are intricate objects that arise in successive refinements of the Volume Conjecture of knots and involve three holomorphic, asymptotic and arithmetic objects. It is expected that the algebraic…
We study the question whether the affine semigroup of integer points in a convex cone can be finitely generated up to symmetries of the cone. We establish general properties of finite generation up to symmetry, and then concentrate on the…
We study finite quasi-quantum groups in their quiver setting developed recently by the first author in arXiv:0902.1620 and arXiv:0903.1472. We obtain a classification of finite-dimensional pointed Majid algebras of finite corepresentation…
We study affine cartesian codes, which are a Reed-Muller type of evaluation codes, where polynomials are evaluated at the cartesian product of n subsets of a finite field F_q. These codes appeared recently in a work by H. Lopez, C.…
We characterize when the monomial maximal ideal of a simplicial affine semigroup ring has a monomial minimal reduction. When this is the case, we study the Cohen-Macaulay and Gorenstein properties of the associated graded ring and provide…
In this note we consider monoidal complexes and their associated algebras, called toric face rings. These rings generalize Stanley-Reisner rings and affine monoid algebras. We compute initial ideals of the presentation ideal of a toric face…