Related papers: Some conditions under which certain types of modul…
The concepts of localizable set, localization of a ring and a module at a localizable set are introduced and studied. Localizable sets are generalization of Ore sets and denominator sets, and the localization of a ring/module at a…
We introduce the concept of multiplicatively closed subsets of a commutative ring $R$ which split an $R$-module $M$ and study factorization properties of elements of $M$ with respect to such a set. Also we demonstrate how one can utilize…
The Gorenstein property in local algebra admits several characterizations via its module category. The goal of this paper is to collect and generalize such characterizations to the relative setting, i.e., to Gorenstein morphisms as defined…
The dynamics of two-level systems in an external periodic field are investigated in general. The necessary conditions of localization are obtained through analysing the time-evolving matrix. It is found that localization is possible if not…
The localization spread gives a criterion to decide between metallic versus insulating behaviour of a material. It is defined as the second moment cumulant of the many-body position operator, divided by the number of electrons. Different…
The study of localizations of groups has concentrated on group theoretic properties which are preserved by localization. In this paper we look at finitely generated soluble groups and determine when the local groups associated with them are…
In previous work we proved that, for categories of free finite-dimensional modules over a commutative semiring, linear compact-closed symmetric monoidal structure is a property, rather than a structure. That is, if there is such a…
Open discrete mappings with a modulus condition in metric spaces are considered. Some results related to local behavior of mappings as well as theorems about continuous extension to a boundary are proved.
Given a non-unit, non-zero-divisor, central element $x$ of a ring $\Lambda$, it is well known that many properties or invariants of $\Lambda$ determine, and are determined by, those of $\Lambda / x \Lambda$ and $\Lambda_x$. In the present…
In this article we discuss Bousfield localization, beginning with definitions in terms of mapping spaces and working up to a discussion of how they can be constructed when we have access to the small object argument. We also discuss…
This paper gives generalization of a notion of supplemented module. Here, we utilize some algebraic properties like supplemented, amply supplemented and local modules in order to obtain the generalization. Other properties that are…
We study the local properties of Artin stacks and their good moduli spaces, if they exist. We show that near closed points with linearly reductive stabilizer, Artin stacks formally locally admit good moduli spaces. We also give conditions…
It is known that graded cyclic modules over $S=K[x,y]$ have the Weak Lefschetz Property (WLP). This is not true for non-cyclic modules over $S$. The purpose of this note is to study which conditions on $S$-modules ensure the WLP. We give an…
Using approximations, we give several characterizations of separability of bimodules. We also discuss how separability properties can be used to transfer some representation theoretic properties from one ring to another one: contravariant…
Local conditions for the direct summands of a persistence module to belong to a certain class of indecomposables have been proposed in the 2-parameter setting, notably for the class of indecomposables called block modules, which plays a…
We show that silting modules are closely related with localisations of rings. More precisely, every partial silting module gives rise to a localisation at a set of maps between countably generated projective modules and, conversely, every…
We derive extensions of the monomialization theorems for morphisms of varieties in our earlier work. In this note we show that a local monomialization can be found which satisfies stronger local conditions. Some comments are made about how…
It is proved that localizations of injective $R$-modules of finite Goldie dimension are injective if $R$ is an arithmetical ring satisfying the following condition: for every maximal ideal $P$, $R_P$ is either coherent or not semicoherent.…
It is proved that localizations of injective $R$-modules of finite Goldie dimension are injective if $R$ is an arithmetical ring satisfying the following condition: for every maximal ideal $P$, $R_P$ is either coherent or not semicoherent.…
This informal note provides some elementary examples to motivate the local structural results of [1] on the moduli space of genus one stable maps to projective space. The hope is that these examples will be helpful for graduate students to…