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Intersection of two ideals of a ring R
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Qn. Show that the intersection of two ideals of a ring R is an ideal
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- Eli
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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!
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!
0
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