Category:Definitions/Additive Inverses

This category contains definitions related to Additive Inverses.
Related results can be found in Category:Additive Inverses.

Additive Inverse in Ring

Let $\struct {R, +, \circ}$ be a ring whose ring addition operation is $+$.

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

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

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

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

Additive Inverse in Field

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 $R$.

Additive Inverse of Number

The concept is often encountered in the context of numbers:

Let $\Bbb F$ be one of the standard number systems: $\N$, $\Z$, $\Q$, $\R$, $\C$.

Let $a \in \Bbb F$ be any arbitrary number.

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

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