An integral domain is a ring with no zero divisors that has this property. Division algebras where this holds are fields. The symmetric group S3 is the smallest group where this doesn't hold, and all cyclic groups have this p
An integral domain is a ring with no zero divisors that has this property. Division algebras where this holds are fields. The symmetric group S3 is the smallest group where this doesn't hold, and all cyclic groups have this property. Unlike addition and multiplication in fields, groups do not necessarily have this property, and when this holds for a group it is called abelian. Matrix multiplication does not have this property nor does subtraction of real numbers which has the anti-form of this property, but it holds for a related operation. For 10 points, name this property that when applied to addition means that A + B = B + A.
An integral domain is a ring with no zero divisors that has this property.
commutative [accept word forms; accept abelian before mentioned]