Boolean ring
By Wedderburn's theorem, every finite division ring is commutative, and therefore a finite field. Another condition ensuring commutativity of a ring, due to Jacobson, is the following: for every element "r" of "R" there exists an integer such that . If, "r"2 = "r" for every "r", the ring is called Boolean ring. More general conditions which guarantee commutativity of a ring are also known.