Field (mathematics)

A ring where multiplication is commutative and there is always an inverse.

A field can be seen as an Abelian group that has two group operations defined on it: addition and multiplication.

And then, besides each of the two operations obeying the group axioms individually, and they are compatible between themselves accordin to the distributive property.

Basically the nicest, least restrictive, 2-operation type of algebra.

Examples:

real numbers
rational numbers

 Ancestors

Ring
Group
Algebra
Area of mathematics
Mathematics
Ciro Santilli's Homepage

 Incoming links

Algebraic structure
Bilinear map
Complex number
Distributive property
Division ring
Elliptic curve
Elliptic curve point addition
General linear group
Isomorphism
Lagrangian density
Not every $x$ belongs to the elliptic curve over a non quadratically closed field
Polynomial over a ring
Ring
Underlying field of a vector space

 Synonyms

Field