In algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a nonzero ring[1] in which every nonzero element a has a multiplicative inverse, that is, an element generally denoted a–1, such that a a–1 = a–1 a = 1. So, division may be defined as a / b = a b–1, but this notation is generally avoided, as one may have a b–1 ≠ b–1 a.