An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the element a is denoted -a (minus a). The symbols and terminology are borrowed from the additive groups of numbers: the ring of integers Z, the field of rational numbers Q, the field of real numbers R, and the field of complex numbers C are all additive groups. In general, every ring and every field is an additive group. An important class of examples is given by the polynomial rings with coefficients in a ring R.

additive identity | additive inverse | multiplicative group