Related papers: Rings of simple range 2

For the second fundamental representation of the general linear group over a commutative ring $R$ we construct straightforward and uniform polynomial expressions of elementary generators as products of elementary conjugates of an arbitrary…

In this paper we introduce the concept of purely infinite rings, which in the simple case agrees with the already existing notion of pure infiniteness. We establish various permanence properties of this notion, with respect to passage to…

We investigate the standard graded $k$-algebras over a field $k$ of characteristic zero for which general linear forms are exact zero divisors. We formulate a conjecture regarding the Hilbert function of such rings. We prove our conjecture…

Let R be a commutative ring with identity and M be an R-module. In this paper, we will introduce the concept of 2-irreducible (resp., strongly 2- irreducible) submodules of M as a generalization of irreducible (resp., strongly irreducible)…

The reduced divisor class group of a normal Cohen--Macaulay graded domain together with its torsion number is introduced. They are studied in detail especially for normal affine semigroup rings.

We study the basis property of systems of exponentials with frequencies belonging to 'simple quasicrystals'. We show that a diophantine condition is necessary and sufficient for such a system to be a Riesz basis in L^2 on a finite union of…

When we consider a finite abelian group acting linearly on a polynomial ring, we can find monomial generators for the subring of invariants. By Noether's degree bound and Hilbert's finiteness theorem, we know that there are finitely many…

We define pullback and separated presentations of modules over pullback rings, and, if the ring is a pullback of epimorphisms over a semisimple ring, an algorithm reducing such a presentation of a module to an $R$-diagram. The latter is the…

We characterize the idempotent stable range one $2\times 2$ matrices over commutative rings and in particular, the integral matrices with this property. Several special cases and examples complete the subject.

In this note, we revisit certain results from a previous work of the second author concerning $z$-ideals of semirings. We demonstrate that the assumption of the semiring being a bzi-semiring can be dispensed with. Additionally, we propose a…

In this paper, we study rational sections of the relative Picard variety of a linear system on a smooth projective variety. Specifically, we prove that if the linear system is basepoint-free and the locus of non-integral divisors has…

We determine the minimal number of separating invariants for the invariant ring of a matrix group $G < \mathrm{GL}_n(\mathbb{F}_q)$ over the finite field $\mathbb{F}_q$. We show that this minimal number can be obtained with invariants of…

We consider finite dimensional representations of the dihedral group $D_{2p}$ over an algebraically closed field of characteristic two where $p$ is an odd integer and study the degrees of generating and separating polynomials in 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…

Let $A$ be an algebra over a commutative ring $k$. We prove that braidings on the category of $A$-bimodules are in bijective correspondence to canonical R-matrices, these are elements in $A\ot A\ot A$ satisfying certain axioms. We show that…

In this paper, we will introduce two generalizations of second submodules of a module over a commutative ring and explore some basic properties of these classes of modules.

Brion proved that the valuation cone of a complex spherical variety is a fundamental domain for a finite reflection group, called the little Weyl group. The principal goal of this paper is to generalize this fundamental theorem to fields of…

Recent proofs of classical theorems in polynomial algebra and functional analysis are discussed, which use tools from the topology of real manifolds. Simpler proofs were discovered in the new century, of the Hilbert Nullstellensatz, and the…

We define a new class of rings parameterized by binary forms of a certain type, and give an effective lower bound for the number of such rings whose discriminant is less than a bound $X$. We also obtain a lower bound for the number of…

This paper introduces an inner product on chain complexes of finite simplicial complexes that is well-adapted to the harmonic study of subdivisions. Its definition utilizes a decomposition of the chain spaces that suggests a sequence of…