Given a ring $R$ and some index set $I$, why is the sum/product of ideals are defined for finite sums/products?
Sum of ideals $\sum_{i \in I}I_i=\{\sum{x_i}: i \in I \}$
Product of ideals $\prod_{i \in I}I_i=\{\prod{x_i}: i \in I \} $
2026-04-06 17:51:45.1775497905
Why the sum of the product of ideals are defined as finite sums/products?
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