Resources for learning about this property:

• F. W. Anderson and K. R. Fuller. Rings and categories of modules. (2012) @ Chapter 8, Section 30
• T.-Y. Lam. Lectures on modules and rings. (2012) @ Sections 15, 16
• W. K. Nicholson and M. F. Yousif. Quasi-Frobenius Rings. (2003) @ .

Metaproperties:

This property has the following metaproperties

• Morita invariant
• passes to matrix rings
• passes to $eRe$ for any full idempotent $e$
• stable under finite products

This property does not have the following metaproperties

• passes to polynomial rings (counterexample)