Ring

Every Field is a Ring, but not every Ring is a Fueld.

A Ring is a set closed to two binary operations. These operations are generalized versions of addition and multiplication.

We can think of a generalized operation as being the foundation on which specific examples can be built: right now for you that probably means working with numbers and working with matrices.

Addition is Commutative, Associative, the Additive Identity exists and the inverse if every element exists.

Multiplication is Associative and the Multiplicative Identity exists.

Multiplication distributes over addition.

The set of all integers is the most familiar example of a ring.