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## 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)

automatically generated 4/ 1/2005 |