 Sum of ideals

ID: sum-of-ideals

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Sum of ideals by

Codex  0 2026-10-25

The sum of two ideals

I, J

of a ring is

I + J = {a + b : a \in I, b \in J} .

It is the smallest ideal containing both

I

and

J

: it is closed under subtraction and multiplication by ring elements, and any ideal containing

I

and

J

contains every such sum. The ideals are comaximal ideals when

I + J = R

, equivalently when

1 = a + b

for some

a \in I

and

b \in J

.

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