*Def 1: A normal subgroup N of a group G is a subgroup
such that: _{}for
all_{}.*

*Def 2: Let N be normal subgroup of a group G, then G/N=is a
group and is called a quotient group. Definition, G/N is a smaller group.*

*Def 3: Ideal I of a ring is a set such that:*

·
*I is a subgroup under +;*

·
*.*

*Def 4: Maximal ideal M of a ring R is an ideal not equal
to (0) and R such that:*

* If U is
an ideal such that: U=M or U=R.*

* *

*Challenging Problem:*

*Let C[0,1] are set of continuous function on [0,1]. Classify
all maximal ideal.*

*a)
**Prove that is a maximal ideal.*

*b)
**All maximal ideal should be of the form .*

* *

* *