Definition:Ring Negative
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Definition
Let $\struct {R, +, \circ}$ be a ring whose zero is $0_R$.
Let $x \in R$.
The inverse of $x$ with respect to the addition operation $+$ in the additive group $\struct {R, +}$ of $R$ is referred to as the (ring) negative of $x$ and is denoted $-x$.
That is, the (ring) negative of $x$ is the element $-x$ of $R$ such that:
- $x + \paren {-x} = 0_R$
Sources
- 1964: Iain T. Adamson: Introduction to Field Theory ... (previous) ... (next): Chapter $\text {I}$: Elementary Definitions: $\S 1$. Rings and Fields
- 1969: C.R.J. Clapham: Introduction to Abstract Algebra ... (previous) ... (next): Chapter $1$: Integral Domains: $\S 3$. Definition of an Integral Domain
- 1978: Thomas A. Whitelaw: An Introduction to Abstract Algebra ... (previous) ... (next): $\S 54$. The definition of a ring and its elementary consequences