A ring is a set R equipped with two binary operations + (addition) and ⋅ (multiplication) satisfying the following three sets of axioms, called the ring …

Dedekind
The study of rings originated from the theory of polynomial rings and the theory of algebraic integers. … See more

Products and powers
For each nonnegative integer n, given a sequence $${\displaystyle (a_{1},\dots ,a_{n})}$$ of … See more

Direct product
Let R and S be rings. Then the product R × S can be equipped with the following natural ring structure: See more

The most familiar example of a ring is the set of all integers $${\displaystyle \mathbb {Z} ,}$$ consisting of the numbers See more

Commutative rings
• The prototypical example is the ring of integers with the two operations of addition and multiplication.
• The rational, real and complex …

The concept of a module over a ring generalizes the concept of a vector space (over a field) by generalizing from multiplication of vectors with elements of a field ( See more