 A ring is an abelian group that is also a monoid by virtue of having a second operation, called the multiplication of the ring. Zero annihilates, meaning that \(0x = x0 = 0\). Furthermore multiplication distributes over addition (the group operation) in both arguments. That is, \(x(y+z) = xy + xz\) and \((x+y)z = xz + yz\).