operation) and (the inversion operation) that satisfy the group axioms.

Examples

* The additive group: the affine line endowed with addition and opposite as group operations is an algebraic group. It is called the additive group (because its -points are isomorphic as a group to the additive group of ), and usually denoted by .
* The multiplicative group: Let be the affine variety defined by the equation in the affine plane . The functions and are regular on , and they satisfy

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