# Property: (right/left) primitive

Definition: (right primitive) There exists a faithful simple right $R$ module

## Resources for learning about this property:

- F. W. Anderson and K. R. Fuller. Rings and categories of modules. (2012) @ Chapter 4
- N. Jacobson. Basic algebra II. (2012) @ Section 4.1
- T.-Y. Lam. A first course in noncommutative rings. (2013) @ Chapter 4

## Metaproperties:

This property has the following metaproperties

- Morita invariant
- passes to $eRe$ for any full idempotent $e$
- passes to matrix rings

This property

**does not** have the following metaproperties