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Field (mathematics)
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Revision as of 18:12, July 20, 2014
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18:12, July 20, 2014
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→Axioms
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fix a broken math tag
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*Addition axioms
*Addition axioms
*#Closure: If <math>a, b \in F</math> then <math>a + b \in F</math>.
*#Closure: If <math>a, b \in F</math> then <math>a + b \in F</math>.
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*#[[Associative property|Associativity]]: For <math>a, b, c \in F<math>, <math>(a + b) + c = a + (b + c)</math>.
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*#[[Associative property|Associativity]]: For <math>a, b, c \in F<
/
math>, <math>(a + b) + c = a + (b + c)</math>.
*#[[Commutative property|Commutativity]]: For <math>a, b \in F</math> <math>a + b = b + a</math>.
*#[[Commutative property|Commutativity]]: For <math>a, b \in F</math> <math>a + b = b + a</math>.
*#[[Identity Element|Identity]]: There exists an element <math>0 \in F</math> such that <math>a + 0 = 0 + a = a</math> for all <math>a \in F</math>.
*#[[Identity Element|Identity]]: There exists an element <math>0 \in F</math> such that <math>a + 0 = 0 + a = a</math> for all <math>a \in F</math>.
GregG
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