# Property: prime

Definition: The product of nonzero right ideals is nonzero

• 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