Use this tag for questions about division rings in abstract algebra and/or noncommutative algebra.
In abstract algebra, a division ring, also called a skew field, is a ring in which division is possible. Specifically, it is a nonzero ring in which every nonzero element a has a multiplicative inverse, i.e., an element $x$ with $a·x=x·a=1$. A division ring is a type of noncommutative ring.
