Related papers: Serre's Condition R_l for Affine Semigroup Rings

In this article, we define and explore the weak normalization of an affine semigroup. In particular, for a fixed prime integer, we provide a geometric description of the weak normalization of an affine semigroup with respect to that prime,…

We call a ring R pointwise semicommutative if for any element a in R either l(a) or r(a) is an ideal of R. A class of pointwise semicommutative rings is a strict generalization of semicommutative rings. Since reduced rings are pointwise…

Let k be an algebraically closed field of positive characteristic. The goal of this paper is to characterize the proper smooth curves X/k of positive genus g equipped with a k-rational point P such that X\P can be realized as an etale cover…

An affine hypersurface is said to admit a pointwise symmetry, if there exists a subgroup of the automorphism group of the tangent space, which preserves (pointwise) the affine metric h, the difference tensor K and the affine shape operator…

In this paper we study and investigate concerning dependent elements of semiprime rings and prime rings R by using generalized derivation and derivation,when R admsit to satisfy some conditions,we give some results about that.

Consider a finite l-group acting on the affine space of dimension n over a field k, whose characteristic differs from l. We prove the existence of a fixed point, rational over k, in the following cases: --- The field k is p-special for some…

Let A be a supersingular abelian variety over a finite field k. We give an approximate description of the structure of the group A(k) of rational points of A over k in terms of the characteristic polynomial f of the Frobenius endomorphism…

The set of minimal primes of a ring is a very important set as far the spectrum of a ring is concerned as every prime contains a minimal prime. So, knowing the minimal primes is the first (important and difficult) step in describing the…

Fields with only finitely many maximal subrings are completely determined. We show that such fields are certain absolutely algebraic fields and give some characterization of them. In particular, we show that the following conditions are…

Let $C\subset\mathbb{N}^p$ be an integer polyhedral cone. An affine semigroup $S\subset C$ is a $ C$-semigroup if $| C\setminus S|<+\infty$. This structure has always been studied using a monomial order. The main issue is that the choice of…

We describe the shape of the Lyubeznik table of either rings in positive characteristic or Stanley-Reisner rings in any characteristic when they satisfy Serre's condition $S_r$ or they are Cohen-Macaulay in a given codimension, condition…

For any graph, one can construct a ring, called the edge ring, which is a quadratic-monomial generated subring of the Laurent polynomial ring $k[x_1^{\pm 1},\dots,x_n^{\pm 1}]$. In fact, every quadratic-monomial generated subring of this…

Consider an algebraic semigroup $S$ and its closed subscheme of idempotents, $E(S)$. When $S$ is commutative, we show that $E(S)$ is finite and reduced; if in addition $S$ is irreducible, then $E(S)$ is contained in a smallest closed…

Irreducible decompositions of monomial ideals in polynomial rings over a field are well-understood. In this paper, we investigate decompositions in the set of monomial ideals in the semigroup ring A[\mathbb{R}_{\geq 0}^d] where A is an…

Let K be an arbitrary (commutative) field with at least three elements, and let n, p and r be positive integers with r<=min(n,p). In a recent work, we have proved that an affine subspace of M_{n,p}(K) containing only matrices of rank…

Let A be a finite subset of N^n and R[x]_A be the space of real polynomials whose monomial powers are from A. Let K be a compact basic semialgebraic set of R^n such that R[x]_A contains a polynomial that is positive on K. Denote by P_A(K)…

Let $S={\sf k}[X_1,\dots, X_n]$ be a polynomial ring, where ${\sf k}$ is a field. This article deals with the defining ideal of the Rees algebra of squarefree monomial ideal generated in degree $n-2$. As a consequence, we prove that Betti…

Let $F$ be a finite set of monomials of the same degree $d\geq 2$ in a polynomial ring $R=k[x_1,...,x_n]$ over an arbitrary field $k$. We give some necessary and/or sufficient conditions for the birationality of the ring extension…

An affine hypersurface $M$ is said to admit a pointwise symmetry, if there exists a subgroup $G$ of ${\rm Aut}(T_p M)$ for all $p\in M$, which preserves (pointwise) the affine metric $h$, the difference tensor $K$ and the affine shape…

Let $A$ be an $m \times n$ matrix with real entries. Given two proper cones $K_1$ and $K_2$ in $\mathbb{R}^n$ and $\mathbb{R}^m$, respectively, we say that $A$ is nonnegative if $A(K_1) \subseteq K_2$. $A$ is said to be semipositive if…