Again, it is no longer a field, not even an additive group.

As with the previous two examples, this set is no longer a field or additive group.

The additive group of integers has 1 as a generating set.

First, consider the additive group of the field.

For an arbitrary ring , let be the underlying additive group.

Let be additive groups and a multiplicative group, all of prime order .

Néron models does not exist for the additive group.

More generally, the underlying additive group of any vector space over is divisible.

Any subgroup of the additive group of a zero ring is an ideal.

The additive group of p-adic numbers Q is locally compact for any prime number p.

A relatively less known construction allows to define real numbers using only the additive group of integers with different versions.

The additive group of integers is superstable, but not totally transcendental.

This proves that any abelian group is the additive group of some ring.

The additive group G has the affine line A as its underlying scheme.

Ring: a semiring whose additive group is an Abelian group.

The additive groups of R and C are isomorphic.

Denote by the additive group on reals modulo one.

An additive identity is the identity element in an additive group.

For example the additive group of an n-dimensional vector space has a faithful representation as n+1xn+1 matrices.

However, DLP in this additive group is trivial to solve, as can easily be seen.

This includes additive groups, all rings, all fields, and all vector spaces.

This technique uses the pure additive group contributions to correlate the wanted property with an easy accessible property.

An additive group may refer to:

Although not assumed, one can prove that the axioms imply that the additive group is abelian.

When is the additive group of integers, the cosets of are the arithmetic progressions.