Category:Definitions/Examples of Fields
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This category contains definitions of examples of fields in the context of Abstract Algebra.
A field is a non-trivial division ring whose ring product is commutative.
Thus, let $\struct {F, +, \times}$ be an algebraic structure.
Then $\struct {F, +, \times}$ is a field if and only if:
- $(1): \quad$ the algebraic structure $\struct {F, +}$ is an abelian group
- $(2): \quad$ the algebraic structure $\struct {F^*, \times}$ is an abelian group where $F^* = F \setminus \set {0_F}$
- $(3): \quad$ the operation $\times$ distributes over $+$.
Subcategories
This category has the following 4 subcategories, out of 4 total.
F
G
- Definitions/Gaussian Field (1 P)
Pages in category "Definitions/Examples of Fields"
The following 10 pages are in this category, out of 10 total.