[home] [lexicon] [problems] [tests] [courses] [auxiliaries] [notes] [staff]

Mathematics-Online lexicon:

# Fields

 A B C D E F G H I J K L M N O P Q R S T U V W X Y Z overview

A set together with two operations (addition and multiplication) is called field if the following requirements (field axioms) are satisfied:

K1
Associative law with respect to the addition: .
K2
There exists an element so that for all (zero element).
K3
For each there exists an element so that . Often is written instead of (inverse with respect to the addition).
K4
Commutative law with respect to the addition: .
K5
Associative law with respect to the multiplication: .
K6
There exists an element so that for all (identity element).
K7
For each there is an element with (inverse with respect to the multiplication).
K8
Commutative law with respect to the multiplication: .
K9
Distributive law: .

(Authors: Burkhardt/Höllig/Hörner)