Sum of ideals

Builds on Ideal

Summary

Let $R$ be a ring and let $I$ and $J$ be left ideals of $R$ . The sum of $I$ and $J$ is $I + J = \{a + b : a \in I, b \in J\}$ . It is a left ideal, and it is the smallest left ideal that contains $I$ and $J$ .

Remarks

The sum $I + J$ is the ideal generated by $I \cup J$ . In $\mathbb{Z}$ , $m\mathbb{Z} + n\mathbb{Z} = d\mathbb{Z}$ , where $d$ is the greatest common divisor of $m$ and $n$ . The ideals $I$ and $J$ are coprime when $I + J = R$ .

Reading path

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Group concept
Ring definition
Ideal definition
Sum of ideals concept

Where this leads

3 pages build on this one.

Tag	`0MBJVDSK1R`
URI	`m2://0MBJVDSK1R`
Kind	concept
Writing	W0 stub
MSC	13A15
Uses	Ideal

Sum of ideals

Summary

Remarks

Reading path

Where this leads

Further reading

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