Multiplication Module and Retractable Concept

Abstract

In this paper; we study a strong relation between faithful multiplication module and retractable concept. We proved that if M is faithful and cyclic, so is retractable. On the other hand, faithful injective Module with multiplication property gives retractable module. Also, finitely generated semi-simple module over quasi-invariant ring is retractable module. Finally, some definitions, examples and properties have been presented about retractable module.