Finitely cosilting modules

TL;DR

This paper introduces finitely cosilting modules as a new class generalizing cotilting modules, explores their properties, and establishes a Cosilting Theorem related to these modules.

Contribution

It defines finitely cosilting modules, studies their properties, and proves a Cosilting Theorem, advancing the theory of cosilting modules.

Findings

Finitely cosilting modules generalize cotilting modules with specific finiteness conditions.

Properties of finitely cosilting modules are characterized and analyzed.

A Cosilting Theorem induced by finitely cosilting modules is established.

Abstract

The notion of cosilting module was recently introduced as a generalization of the concept of cotilting module. In this paper, it is introduced the notion of finitely cosilting module, i.e. a cosilting module with some finitness conditions, and it is studied some properties of these modules. Moreover, it is given a Cosilting Theorem induced by such a module.