Field
Set
| context | X |
| definiendum | ⟨X,+,∗⟩∈field(X) |
| postulate | ⟨X,+,∗⟩∈divisionRing(X) |
| postulate | ⟨X,∗⟩∈abelianGroup(X) |
Discussion
A field is essentially two compatible abelian groups over a set X, one of which is necessarily commutative. Compatible in the sense of the distributive laws of a ring, which is asymmetrical with respect to “+” and “∗”.
The second requirement destinguishes the division ring from a division ring by requiring commutivity and of the multiplication ∗.
One generally (also) calls F the field.
Theorems
Finite fields are completely determined by their cardinality.
There is a field of cardinality for each pn, p prime.
Reference
Wikipedia: Field
Parents
Subset of
