Field theory MOC

Field

A field is an algebraic structure with operations resembling those of Rational numbers. 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 ring

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

Constructing fields

• Condition for a quotient commutative ring to be a field

Properties

• ^C1
• A field contains modular arithmetic or the rationals

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