Related papers: Weak normality, Gorenstein and Serre's conditions

Let A be a commutative ring, and \a a weakly proregular ideal in A. This includes the noetherian case: if A is noetherian then any ideal in it is weakly proregular; but there are other interesting examples. In this paper we prove the MGM…

We provide a generalization of Jouanolou duality that is applicable to a plethora of situations. The environment where this generalized duality takes place is a new class of rings, that we introduce and call weakly Gorenstein. As a main…

This paper has two parts. In the first part we recall the important role that weak proregularity of an ideal in a commutative ring has in derived completion and in adic flatness. We also introduce the new concepts of idealistic and…

The results of the renormalization group are commonly advertised as the existence of power law singularities near critical points. The classic predictions are often violated and logarithmic and exponential corrections are treated on a…

In this paper, we define and study a particular case of von Neumann regular notion called a weak von Neumann regular ring. It shown that the polynomial ring $R[x]$ is weak von Neumann regular if and only if $R$ has exactly two idempotent…

Our purpose in this work is multifold. First, we provide general criteria for the finiteness of the projective and injective dimensions of a finite module $M$ over a (commutative) Noetherian ring $R$. Second, in the other direction, we…

We give a quasihomogeneity criterion for Gorenstein curves. For complete intersections, it is related to the first step of Vasconcelos' normalization algorithm. In the process, we give a simplified proof of the Kunz-Ruppert criterion.

Let $\underline{x} = x_1,\ldots,x_k$ denote an ordered sequence of elements of a commutative ring $R$. Let $M$ be an $R$-module. We recall the two notions that $\underline{x}$ is $M$-proregular given by Greenlees and May (see \cite{[5]})…

We completely characterize the weak differentiability (or, in other words Gateaux differentiability) of the norm in the spaces of bounded multilinear maps. Also, we obtain a multilinear generalization of the well-known Bhatia-\v{S}emrl…

Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized number representation systems. We explore the concepts of…

Different and distinct notions of regularity for modules exist in the literature. When these notions are restricted to commutative rings, they all coincide with the well-known von-Neumann regularity for rings. We give new characterizations…

We discuss the relation between questions regarding the essential normality of finitely generated essentially spherical isometries and some results and conjectures of Arveson and Guo-Wang on the closure of homogeneous ideals in the m-shift…

This paper considers graded near-rings over a monoid G as a generalizations of the graded rings over groups, introduce certain innovative graded weakly prime ideals and graded almost prime ideals as a generalizations of graded prime ideals…

Let $\xx= x_1,\ldots,x_r$ denote a system of elements of a commutative ring $R$. For an $R$-module $M$ we investigate when $\xx$ is $M$-pro-regular resp. $M$-weakly pro-regular as generalizations of $M$-regular sequences. This is done in…

Weakly stable torsion classes were introduced by the author and Yekutieli to provide a torsion theoretic characterisation of the notion of weak proregularity from commutative algebra. In this paper we investigate weakly stable torsion…

We investigate the almost sure asymptotic properties of vector martingale transforms. Assuming some appropriate regularity conditions both on the increasing process and on the moments of the martingale, we prove that normalized moments of…

The goal of this article is to present the graded weakly $S$-primary ideals and $g$-weakly $S$-primary ideals which are extensions of graded weakly primary ideals. Let $R$ be a commutative graded ring, $S\subseteq h(R)$ and $P$ be a graded…

We find sufficient conditions which imply equality of the finitistic test ideal and test ideal in rings of prime characteristic. Utilizing recent progress from the prime characteristic minimal model program we equate the notions of…

In the set of continuous functions C(X,Y) where Y has a topology close to being discrete, there is an equivalence relation on X which characterizes the quasi-components of X. If Y satisfies weak algebraic conditions with a single binary…

We study the relations between different regularity assumptions in the definition of weak solutions and supersolutions to the porous medium equation. In particular, we establish the equivalence of the conditions $u^m \in L^2_{\rm…