For 10 points, identify this property that requires A plus B equal B plus A for addition.
A monoid with the cancellation property and this property can be embedded into a group via the Grothendieck construction. If two linear transformations are diagonalizable and have this property, then they share an eigenspace. Every finite division ring has this property, and a ring without this property may have unequal left and right (*) ideals. Every simple group with this property has prime order, and the smallest group without this property is the symmetric group S3. Every subgroup is normal for groups with this property, which are known as abelian. For 10 points, identify this property that requires A plus B equal B plus A for addition.
A monoid with the cancellation property and this property can be embedded into a group via the Grothendieck construction.
commutativity [or commutative; prompt on abelian until it is read]