Category:Fields (Abstract Algebra)

This category contains results about fields in the context of abstract algebra.
Definitions specific to this category can be found in Definitions/Fields (Abstract Algebra).

$\struct {F, +, \times}$ 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 $+$.