additive group

additive group (plural additive groups)

1. (mathematics) Any group, or algebraic object that can be regarded as a group, whose binary operation is called addition and denoted +; specifically:
   1. (group theory) Any (often, but not necessarily, abelian) group whose binary operation is called addition.
   2. (algebra) 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.
   3. (category theory) Any group object (such as a group functor, group scheme, etc.), whose binary operation is called addition.

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).