Field theory MOC

Field

A field is an algebraic structure with operations resembling those of . A field consists of an abelian group with identity called addition, and an additional abelian group called multiplication, such that multiplication is distributive over addition #m/def/ring

That is, a field is both a commutative ring and a division ring.

Constructing fields

• for commutative is a field iff is maximal

Properties

• is a field iff it has no nonzero proper ideals
• A field contains or

#state/tidy | #lang/en | #SemBr