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Lecture 1: Review on quotient group, ideal and maximal ideal

 

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 .

 

 

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