Related papers: Growth and Relations in Graded Rings

Let $K$ be a field, $R$ a standard graded $K$-algebra and $M$ be a finitely generated graded $R$-module. The rate of $M$, $rate_R(M)$, is a measure of the growth of the shifts in the minimal graded free resolution of $M$. In this paper, we…

Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…

Ideals in the ring of power series in three variables can be classified based on algebra structures on their minimal free resolutions. The classification is incomplete in the sense that it remains open which algebra structures actually…

The mod-p cohomology ring of a non-trivial finite p-group is an infinite dimensional, finitely presented graded unital algebra over the field with p elements, with generators in positive degrees. We describe an effective algorithm to test…

We establish formulas for computation of the higher algebraic $K$-groups of the endomorphism rings of objects linked by a morphism in an additive category. Let ${\mathcal C}$ be an additive category, and let $Y\ra X$ be a covariant morphism…

Let $K$ be a number field with ring of integers $\mathcal{O}$ and $\alpha\in\mathcal{O}$. For any prime ideal $\mathfrak{p}$ of $\mathcal{O}$, we obtain its higher $\alpha$-Wieferich property, which implies a nonexistence theorem for higher…

Let W be an associative PI-algebra over a field F of characteristic zero. Suppose W is G-graded where G is a finite group. Let exp(W) and exp(W_e) denote the codimension growth of W and of the identity component W_e, respectively. The…

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of…

In this note, we give examples of formal power series satisfying certain conditions that cannot be realized as Hilbert series of finitely generated modules. This answers to the negative a question raised in a recent article by the second…

Let $R$ be an algebra over a commutative ring $k$. Suppose that $R$ is endowed with a descending filtration indexed on an ordered group $(G,<)$ such that the restriction to $k$ is positive. We show that the existence of free algebras on a…

Let $RG$ be the group ring of a finite group $G$ over a commutative ring $R$ with $1$. An element $x$ in $RG$ is said to be skew-symmetric with respect to an involution $\sigma$ of $RG$ if $\sigma(x)=-x.$ A structure theorem for the…

We formulate a notion of "geometric reductivity" in an abstract categorical setting which we refer to as adequacy. The main theorem states that the adequacy condition implies that the ring of invariants is finitely generated. This result…

We prove several numerical radius inequalities for linear operators in Hilbert spaces. It is shown, among other inequalities, that if $A$ is a bounded linear operator on a complex Hilbert space, then \[\omega \left( A \right)\le…

We prove upper and lower bounds for all the coefficients in the Hilbert Polynomial of a graded Gorenstein algebra $S=R/I$ with a quasi-pure resolution over $R$. The bounds are in terms of the minimal and the maximal shifts in the resolution…

In this article, we introduce a relation including ideals of an evolution algebra and hereditary subsets of vertices of its associated graph and establish some properties among them. This relation allows us to determine maximal ideals and…

Let I = (F_1,...,F_r) be a homogeneous ideal of R = k[x_0,...,x_n] generated by a regular sequence of type (d_1,...,d_r). We give an elementary proof for an explicit description of the graded Betti numbers of I^s for any s \geq 1. These…

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of…

Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…

We introduce ring theoretic constructions that are similar to the construction of wreath product of groups. In particular, for a given graph $\Gamma=(V,E)$ and an associate algebra $A,$ we construct an algebra $B=A\, wr\, L(\Gamma)$ with…

Let R be a commutative ring with unity, M be an unitary R-module and {\Gamma} be a simple graph. This research article is an interplay of combinatorial and algebraic properties of M . We show a combinatorial object completely determines an…