The concept of a group has its origin in the set of mappings or permutations, of a set onto itself. So far we have considered sets with one binary operation only. But rings are the motivation which arises from the fact that integers follow a definite pattern with respect to the addition and multiplication. Thus we now aim at studying rings which are algebraic systems with two suitably restricted and related binary operation.

__Definition__**:**

An algebraic structure where is a non-empty set and and are defined operations in , is called a ring if for all in , the following axioms are satisfied:

is an abelian group.

is an semi group.

Multiplication is left as well as right distributive over addition, i.e.

and

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