Curto and Fialkow proved in 1996 that flat positive semidefinite moment matrices always come from a finitely atomic positive measure. The tedious part of the proof is to show that flat moment matrices have always a flat extension. We give a new short argument for this based on Gröbner bases. Résumé. Curto et Fialkow ont démontré en 1996 que les matrices des moments, plates et semidéfinies posit...

Let M be a commutative cancellative atomic monoid. We consider the behavior of the asymptotic length functions ̄̀(x) and L̄(x) on M . If M is finitely generated and reduced, then we present an algorithm for the computation of both ̄̀(x) and L̄(x) where x is a nonidentity element of M . We also explore the values that the functions ̄̀(x) and L̄(x) can attain when M is a Krull monoid with torsion diviso...

we define and studyco-noetherian dimension of rings for which the injective envelopeof simple modules have finite krull-dimension. this  is a moritainvariant dimension that measures how far the ring is from beingco-noetherian. the co-noetherian dimension of certain rings,including commutative rings, are determined. it is shown that the class ${mathcal w}_n$ of rings with co-noetherian dimension...

For a non negative measure $\mu$ with $p$ atoms, we study the relation between Square Root Problem of and problem subnormality ${\tilde W_\mu}$ Aluthge transform associated unilateral weighted shift. We use an approach based on uniquely represented elements in support $\mu*\mu$. first show that if is subnormal, then $2p-1\le card(supp(\mu*\mu))\le [\frac{(p-1)^2+6}{2}]$. rewrite several results...

In this article we give a characterization of monoids for which torsion freeness, ((principal) weak, strong) flatness, equalizer flatness or Condition (E) of finitely generated and (mono) cyclic acts and Condition (P) of finitely generated and cyclic acts implies regularity. A characterization of monoids for which all (finitely generated, (mono) cyclic acts are regular will be given too. We als...

Let $R$ be a commutative Noetherian ring. We prove that  over a local ring $R$ every finitely generated $R$-module $M$ of finite Gorenstein projective dimension has a Gorenstein projective cover$varphi:C rightarrow M$ such that $C$ is finitely generated and the projective dimension of $Kervarphi$ is finite and $varphi$ is surjective.

A ring has bounded factorizations if every cancellative nonunit a∈R can be written as a product of atoms and there is bound λ(a) on the lengths such factorizations. The factorization property one most basic finiteness properties in study non-unique Every commutative noetherian domain factorizations, but it open whether result holds noncommutative setting. We provide sufficient conditions for pr...

An integral domain is atomic if every nonzero nonunit factors into irreducibles. Let R be an domain. We say that a bounded factorization it and for \(x \in R\), there positive integer N such any = a_1 \cdots a_n\) of x irreducibles \(a_1, \dots , in R, the inequality \(n \le N\) holds. In addition, we finite only finitely many ways (up to order associates). The notions domains were introduced b...