# Introduction to Rings in Algebra

The concept of a group has its origin in the set of mappings or permutations of a set unto 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 addition and multiplication. Thus we now aim at studying rings which are algebraic systems with two suitably restricted and related binary operations.

__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 a semi group.

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

and

andrew makatu

July 23@ 6:56 pmits enjoying how a ring comes about: from a set to a group (4 properties) from group to a ring (8 properties) and then a field