A new approach to (dual) Rickart modules via isomorphisms

Abstract

In the past few decades, researchers have found that studying modules using endomorphisms is a powerful and useful tool. This has led to valuable works in this field. Recently, the study of (dual) Rickart modules has become an important approach as they are deeply connected to endomorphisms. Building on this work, the authors introduce a new perspective on (dual) Rickart modules using isomorphism. We also define virtually (dual) Rickart modules. It is shown that rings with all modules virtually Rickart are semisimple rings. The paper includes various examples to illustrate the concepts presented.

Keywords

• annihilator
• dual rickart module
• virtually rickart module
• virtually dual rickart module
• endomorphism ring
• primary 16d10, 6d40
• secondary 16d90