Definition:Additive Group of Field
This page is about Additive Group of Field. For other uses, see Additive Group.
Definition
Let $\struct {F, +, \times}$ be a field.
The group $\struct {F, +}$ is known as the additive group of $F$.
Also defined as
Some sources make special issue of the nature of a group when its underlying set is a subset of, or derived directly from, numbers themselves.
In such treatments, a group whose operation is addition is then referred to as an additive group.
On $\mathsf{Pr} \infty \mathsf{fWiki}$ we consider all groups, whatever their nature, to be instances of the same abstract concept, and therefore make no such distinction.
Some sources confuse and muddy the water still further by calling an additive group any group whose notation is such that it uses $+$ as the symbol to denote the group operation and use $0$ to denote the identity.
Also see
- Definition:Additive Group of Rational Numbers
- Definition:Additive Group of Real Numbers
- Definition:Additive Group of Complex Numbers
- Definition:Additive Group of Integers
- Definition:Additive Group of Integer Multiples
- Definition:Additive Group of Integers Modulo m
Sources
There are no source works cited for this page. Source citations are highly desirable, and mandatory for all definition pages. Definition pages whose content is wholly or partly unsourced are in danger of having such content deleted. To discuss this page in more detail, feel free to use the talk page. |