Definition:Additive Group of Ring

Definition
Let $\struct {R, +, \circ}$ be a ring.

The group $\struct {R, +}$ is known as the additive group of $R$.

Also denoted as
Some sources write $\struct {R, +}$ as $R^+$ but this can be confused with the set of positive elements $R_+$ of an ordered ring.

Also see

 * Definition:Additive Group of Integers
 * Definition:Additive Group of Integer Multiples
 * Definition:Additive Group of Integers Modulo m


 * Definition:Additive Group of Field


 * Definition:Additive Group of Rational Numbers
 * Definition:Additive Group of Real Numbers
 * Definition:Additive Group of Complex Numbers