so lets see what a field is according to wikipedia,
field > a commutative ring which contains a multiplicative inverse for every nonzero element
but what's a commutative ring?
commutative ring > a ring in which the multiplication operation is commutative
but what's a ring?
ring > an abelian group with a second binary operation that is associative and is distributive over the abelian group operation
but what's an abelian group
abelian group> a group in which the result of applying the group operation to two group elements does not depend on their order.
but what's a group?
group > a set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms, namely closure, associativity, identity and invertibility
adding it all up
field: a set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms, namely closure, associativity, identity and invertibility in which the result of applying the set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms, namely closure, associativity, identity and invertibility operation to two set of elements together with an operation that combines any two of its elements to form a third element also in the set while satisfying four conditions called the group axioms, namely closure, associativity, identity and invertibility elements does not depend on their order in which the multiplication operation is commutative which contains a multiplicative inverse for every nonzero element.
Topic: recursive definition decomposition (Read 2235 times)
