Some conditions under which certain types of modules possess localization property

TL;DR

This paper investigates conditions that ensure modules retain specific properties after localization at multiplicative closed sets, aiming to identify when properties are preserved or can be transferred between modules and their localizations.

Contribution

It provides new conditions under which certain module properties are preserved or transferred through localization at multiplicative closed sets.

Findings

Identifies conditions for property preservation under localization

Establishes criteria for when modules possess localization properties

Provides several new sufficient conditions for localization property

Abstract

By a localization property we mean a property that preserved under localizing modules at multiplicative closed sets. The aim of this paper is to find conditions under which we can transfere a certain property of a given module to its localization at multiplicative closed sets and conversely, that means we determine those conditions which make a given property of a module as a localization property, so we give several conditions under which certain types of modules posses localization property.