*If ''R'' is a [[ring with unity]], i.e., there exists a multiplicative identity '''1''', then the characteristic is already given by the smallest ''r'' such that ''r'' * '''1''' = 0. If no such ''r'' exists, the characteristic is defined as zero. | *If ''R'' is a [[ring with unity]], i.e., there exists a multiplicative identity '''1''', then the characteristic is already given by the smallest ''r'' such that ''r'' * '''1''' = 0. If no such ''r'' exists, the characteristic is defined as zero. |