On the notion of 'retractable modules' in the context of algebras

TL;DR

This survey explores the concept of retractable modules within algebra theory, illustrating how classical results can be reinterpreted through module theory and highlighting open questions in the field.

Contribution

It provides a comprehensive overview of retractable modules in algebra, connecting classical results with module-theoretic perspectives and proposing future research directions.

Findings

Classical algebra results can be interpreted via retractable modules

The survey identifies key properties and applications of retractable modules

Open questions in the theory of retractable modules are discussed

Abstract

This is a survey on the usage of the module theoretic notion of a "retractable module" in the study of algebras with actions. We explain how classical results can be interpreted using module theory and end the paper with some open questions.