In mathematics, rings are algebraic structures that generalize fields: multiplication need not be commutative and
Formally, … See more

The most familiar example of a ring is the set of all integers consisting of the numbers
The axioms of a ring were elaborated as a generalization of familiar properties of addition and multiplication of integers.
Some basi… See more

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 introduc… See more

• The prototypical example is the ring of integers with the two operations of addition and multiplication.
• The rational, real and complex numbers are commutative rings of a type called fields.… See more

For each nonnegative integer n, given a sequence of n elements of R, one can define the product recursively: let P0 = 1 and let Pm = Pm−1am for 1 ≤ m ≤ n.
As a special case, one can define nonnegativ… 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 (scalar multiplication) to multiplication with eleme… See more

Let R and S be rings. Then the product R × S can be equipped with the following natural ring structure:
for all r1, r2 in R and s1, s2 in S. The ring R × S with the above operations of addition and multipli… See more