Definition:Additive Notation
Merge this with the similar subsection in Definition:Abelian Group.
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Definition
Additive notation is a convention often used for representing a commutative binary operation of an algebraic structure. The symbol used for the operation is $+$.
Let $\left({S, +}\right)$ be such an algebraic structure, and let $x, y \in S$.
- $x + y$ is used to indicate the result of the operation $+$ on $x$ and $y$.
- $e$ or $0$ is used for the identity element. Note that in this context, $0$ is not a zero element.
- $- x$ is used for the inverse element.
- $n x$ is used to indicate the $n$th power of $x$.
This notation is usual in group theory when discussing a general abelian group.
It is also usual in ring theory for the ring addition.
In this context, the inverse of an element $x$ is often referred to as the negative of $x$.
Also see
Sources
- Iain T. Adamson: Introduction to Field Theory (1964)... (previous)... (next): $\S 1.1$
- J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 4.1$
- J.A. Green: Sets and Groups (1965)... (previous)... (next): $\S 4.5 \ (1)$
- B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra (1970): $\S 1.1$: Definitions $1.1 \ \text{(b)}$
- Thomas A. Whitelaw: An Introduction to Abstract Algebra (1978)... (previous)... (next): $\S 31$
- John F. Humphreys: A Course in Group Theory (1996): $\S 1$
