# Property: Boolean

Definition: For every $x\in R$, $x^2=x$.

• N. Jacobson. Basic algebra I. (2012) @ Section 8.5

## Metaproperties:

This property has the following metaproperties
• passes to $eRe$ for any full idempotent $e$
• passes to $eRe$ for any idempotent $e$
• passes to localizations
• passes to quotient rings
• passes to subrings
• passes to the center
• stable under finite products
• stable under products
This property does not have the following metaproperties
• Morita invariant (counterexample needed)
• passes to matrix rings (counterexample needed)
• passes to polynomial rings (counterexample needed)
• passes to power series ring (counterexample needed)