Definition:Additive Inverse/Ring
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This page is about Additive Inverse of Ring. For other uses, see Additive Inverse.
Definition
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 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 $-a$:
- $a + \paren {-a} = 0$
Sources
- 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): additive inverse (in a ring or group)