Related papers: The index of a numerical semigroup ring

The total embedding distributions of a graph is consisted of the orientable embeddings and non- orientable embeddings and have been know for few classes of graphs. The genus distribution of Ringel ladders is determined in [Discrete…

In this paper we present and study the numerical duplication of a numerical semigroup, a construction that, starting with a numerical semigroup $S$ and a semigroup ideal $E\subseteq S$, produces a new numerical semigroup, denoted by…

Let $p$ be a prime number and let $n$ be a non-zero natural number. We compute the descending Loewy series of the algebra $R\_n/pR\_n$, where $R\_n$ denotes the ring of virtual ordinary characters of the symmetric group $S\_n$.

Let $A$ be a right Ore domain, $Z(A)$ be the center of $A$ and $Q_r(A)$ be the right total ring of fractions of $A$. If $K$ is a field and $A$ is a $K$-algebra, in this short paper we prove that if $A$ is finitely generated and ${\rm…

We characterize intermediate $\mathbb{R}$-algebras $A$ between the ring of semialgebraic functions ${\mathcal S}(X)$ and the ring ${\mathcal S}^*(X)$ of bounded semialgebraic functions on a semialgebraic set $X$ as rings of fractions of…

Let $S$ be the numerical semigroup generated by three consecutive numbers $a,a+1,a+2$, where $a\in\mathbb{N}$, $a\geq 3$. We describe the elements of $S$ whose factorizations have all the same length, as well as the set of factorizations of…

In this paper we study endomorphism rings of finite global dimension over a ring associated to a numerical semigroup. We construct these endomorphism rings in two ways, called the lazy and greedy construction. The first main result of this…

Given a numerical semigroup ring $R=k[\![S]\!]$, an ideal $E$ of $S$ and an odd element $b \in S$, the numerical duplication $S \! \Join^b \! E$ is a numerical semigroup, whose associated ring $k[\![S \! \Join^b \! E]\!]$ shares many…

We prove in particular that the Gorenstein numerical semigroup ring generated by (36,48,50,52,56,60,66,67,107,121,129,135) has a transcendental series of Betti numbers. The methods of proofs are the theory of Golod homomorphism and the…

If $S=<d_1,...,d_\nu>$ is a numerical semigroup, we call the ring $\C[S]=\C[t^{d_1},...,t^{d_\nu}]$ the semigroup ring of $S$. We study the ring of differential operators on $\C[S]$, and its associated graded in the filtration induced by…

Let $R$ be a commutative ring and $M$ be an $R$-module, and let $I(R)^*$ be the set of all non-trivial ideals of $R$. The $M$-intersection graph of ideals of $R$, denoted by $G_M(R)$, is a graph with the vertex set $I(R)^*$, and two…

For some numerical semigroup rings of small embedding dimension, namely those of embedding dimension 3, and symmetric or pseudosymmetric of embedding dimension 4, presentations has been determined in the literature. We extend these results…

We find the index of symmetry for all solvable three-dimensional Lie groups with a left-invariant metric. When combined with the work of Reggiani on unimodular three-dimensional Lie groups, the index of symmetry is then known for all…

In a semiprime ring, von Neumann regular elements are determined by their inner inverses. In particular, for elements $a,b$ of a von Neumann regular ring $R$, $a=b$ if and only if $I(a)=I(b)$, where $I(x)$ denotes the set of inner inverses…

Let M be an irreducible Riemannian symmetric space. The index of M is the minimal codimension of a (non-trivial) totally geodesic submanifold of M. We prove that the index is bounded from below by the rank of the symmetric space. We also…

This paper studies Young diagrams of symmetric and pseudo-symmetric numerical semigroups and describes new operations on Young diagrams as well as numerical semigroups. These provide new decompositions of symmetric and pseudo-symmetric…

The supremum of reduction numbers of ideals having principal reductions is expressed in terms of the integral degree, a new invariant of the ring, which is finite provided the ring has finite integral closure. As a consequence, one obtains…

The concept of integral as an inverse to that of derivation was already introduced for rings and recently also for lattices. Since semirings generalize both rings and bounded distributive lattices, it is natural to investigate integration…

We calculate the metric dimension of the total graph of a direct product of finite commutative antinegative semirings with their sets of zero-divisors closed under addition.

Let $D$ be a division algebra, finite-dimensional over its center, and $R=D[t;\sigma,\delta]$ a skew polynomial ring. Using skew polynomials $f\in R$, we construct division algebras and a generalization of maximum rank distance codes…