additive group

Noun

 * 1)  Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:
 * 2)  Any (often, but not necessarily, abelian) group whose binary operation is called addition.
 * 3)  Any of certain algebraic objects (ring, field or vector space, etc., whose definition includes a commutative operation called addition) regarded as a group under addition.
 * 4)  Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.

Usage notes
Borrowing terminology and notation from arithmetic, the additive inverse of an element a is called minus a (denoted −a), and the additive identity is called zero (0).

Translations

 * Finnish: additiivinen ryhmä, yhteenlaskuryhmä
 * German: additive Gruppe
 * Spanish: grupo aditivo