Ring:-
An algebraic system (R,+,.) consisting of a
non-empty set R with two binary composition (to be denoted by addition and
multiplication) is called a ring if following axiom are satisfied-
(R,+) is
an abelian group.
1- Closure axiom
2- Associative law
3- Identity element
4- Inverse axiom
(R,.) is
a semi group.
1- Closure axiom
2- Associative law
3- Multiplication distributive over
addition i.e.
a.(b+c)=a.b+a.c, ∀ a, b, c∊R
and (b+c).a=b.a+c.a, ∀a, b, c∊R
