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Intersection of two ideals of a ring R

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John Linus B,
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#1

Qn. Show that the intersection of two ideals of a ring R is an ideal
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Heslon
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Eli
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#3

Let me define what is ring and ideal in abstract algebra context.

A ring is a set with two binary operations of and . , such that:

(i) is an abelian group,

(ii) is closed under multiplication and ,

(iii) .

Usually, there is left ideal, right ideal and 2-sided ideal, but, here we mean 2-sided.

A subset of a ring is called an ideal provided it is a subgroup of the additive group and if and then:

(i) ,

(ii) ,

(iii) .

Hope this will give others a highlight and a hint to answer the question!
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