Related papers: On the multiplication map of a multigraded algebra

Given a t.u.p.-semigroup (two unique product semigroup) $X$, we show if $R$ is an $X$-graded ring then both its nilradical and Jacobson radical are homogeneous. This partially answers questions of Smoktunowicz and Jespers.

In this paper, we study an impact of Leibniz algebras on the algebraic structure of $\mathbb{N}$-graded vertex algebras. We provide easy ways to characterize indecomposable non-simple $\mathbb{N}$-graded vertex algebras…

Let $a,b$ be elements in a unital C$^*$-algebra with $0\leq a,b\leq 1$. The element $a$ is absolutely compatible with $b$ if $$\vert a - b \vert + \vert 1 - a - b \vert = 1.$$ In this note we find some technical characterizations of…

Let $R$ be a standard graded Noetherian algebra over an Artinian local ring. Motivated by the work of Achilles and Manaresi in intersection theory, we first express the multiplicity of $R$ by means of local $j$-multiplicities of various…

We found a necessary and sufficient condition for the existence of the tensor product of modules over a vertex algebra. We defined the notion of vertex bilinear map and we provide two algebraic construction of the tensor product, where one…

A Lie algebra $L$ is said to be $(\Theta_{n},sl_{n})$-graded if it contains a simple subalgebra $\mathfrak{g}$ isomorphic to $sl_{n}$ such that the $\mathfrak{g}$-module $L$ decomposes into copies of the adjoint module, the trivial module,…

First we prove that any inner automorphism in the stabilizer of a graded-simple unital associative algebra whose grading group is abelian is the conjugation by a homogeneous element. Now consider a grading by an abelian group on an…

Let us consider a polynomial algebra in three variables equipped with an integer grading. We construct a system of group-generating automorphisms that preserve a given grading.

We formulate and prove a combinatorial criterion to decide if an A-hypergeometric system of differential equations has a full set of algebraic solutions or not. This criterion generalises the so-called interlacing criterion in the case of…

We define a new grading, that we call the "level grading", on the algebra of polynomials generated by the derivatives $u_{k+i}=\partial^{k+i}u/\partial x^{k+i}$ over the ring $K^{(k)}$ of $C^{\infty}$ functions of $u,u_1,...,u_k$. This…

Patterns on numerical semigroups are multivariate linear polynomials, and they are said to be admissible if there exists a numerical semigroup such that evaluated at any nonincreasing sequence of elements of the semigroup gives integers…

We consider the recursive equation ``x(n+1)=A(n)x(n)'' where x(n+1) and x(n) are column vectors of size k and where A(n) is an irreducible random matrix of size k x k. The matrix-vector multiplication in the (max,+) algebra is defined by…

We study partially and totally associative ternary algebras of first and second kind. Assuming the vector space underlying a ternary algebra to be a topological space and a triple product to be continuous mapping we consider the trivial…

We study the structure of a $3-$Leibniz algebra $T$ graded by an arbitrary abelian group $G,$ which is considered of arbitrary dimension and over an arbitrary base field $\bbbf.$ We show that $T$ is of the form $T=\uu\oplus\sum_jI_j,$ with…

Let A be a unitary algebra and G be a finite abelian group. Then a G-graded algebra is merely a G-algebra and viceversa because of the fact that G and its group of characters G* are isomorphic. This fact is no longer true if we substitute G…

The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…

For an associative algebra $A$ a skew-symmetric sum of $n!$ products of $n$ elements of $A$ in all possible order is called $n$-commutator. We consider $A$ as $n$-ary algebra under $n$-commutator. We prove that it has an identity of…

For any triple $(\mu,\lambda,\alpha)$ of complex numbers and an $\mathfrak a$-module ${V}$, a class of non-weight modules $\mathcal{M}\big(V,\mu,\Omega(\lambda,\alpha)\big)$ over the Virasoro algebra $\mathcal L$ is constructed in this…

Suppose $A$ is a graded associative algebra over a field, $I$ is its ideal generated by a set $\alpha$ of homogeneous elements, and B = A/I. In this note, some inequalities between Hilbert series of algebras $A,B$ and the number of elements…

Necessary and sufficient conditions are given for a $G$-graded simple module over a unital associative algebra, graded by an abelian group $G$, to be isomorphic to a loop module of a simple module, as well as for two such loop modules to be…