Definition:Field (Abstract Algebra)/Addition

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The distributand $+$ of a field $\struct {F, +, \times}$ is referred to as field addition, or just addition.

Additive Group

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

Additive Inverse

Let $\struct {F, +, \times}$ be a field whose addition operation is $+$.

Let $a \in R$ be any arbitrary element of $F$.

The additive inverse of $a$ is its inverse under addition, denoted $-a$:

$a + \paren {-a} = 0_F$

where $0_F$ is the zero of $R$.