Definition: $xy=yx$ for all $x$ and $y$ in the ring

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- passes to subrings
- stable under finite products
- stable under products
- passes to $eRe$ for any idempotent $e$
- passes to $eRe$ for any full idempotent $e$
- passes to quotient rings
- passes to localizations

- Morita invariant (counterexample)
- passes to matrix rings (counterexample)