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

Dedekind
The study of rings originated from the theory of polynomial rings and the theory of algebraic integers. In 1871, Richard Dedekind defined the concept of the ring of integers of a number field. In this context, he … See more

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

The most familiar example of a ring is the set of all integers $${\displaystyle \mathbb {Z} ,}$$ consisting of the numbers
$${\displaystyle \dots ,-5,-4,-3,-2,-1,0,1,2,3,4,5,\dots }$$ See more

Commutative rings
• The prototypical example is the ring of integers with the two operations of addition and multiplication. See more

Products and powers
For each nonnegative integer n, given a sequence $${\displaystyle (a_{1},\dots ,a_{n})}$$ of n elements of R, one can define the product 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