Definition:Field Negative
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Definition
Let $\struct {F, +, \times}$ be a field whose zero is $0_F$.
Let $x \in F$.
The inverse of $x$ with respect to the addition operation $+$ in the additive group $\struct {F, +}$ of $F$ is referred to as the (field) negative of $x$ and is denoted $-x$.
That is, the (field) negative of $x$ is the element $-x$ of $F$ such that:
- $x + \paren {-x} = 0_F$
Sources
- 1971: Allan Clark: Elements of Abstract Algebra ... (previous) ... (next): Chapter $3$: Field Theory: Definition and Examples of Field Structure: $\S 87$