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Talk:Principal ideal

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moved statement

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I moved this here:

It becomes natural to ask of any integral domain R "how many" ideals are not principal, or "how far" R is from being a PID.

The ideal class group is a construction which answers this question in a more or less precise sense. It can be defined for any integral domain.

The discussion on Talk:ideal class group seems to indicate that the ideal class group cannot be defined for all integral domains, only for Dedekind domains. AxelBoldt 00:58 Dec 1, 2002 (UTC)

two-sided principal ideal

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The article defines:

  • a two-sided principal ideal of is a subset of all finite sums of elements of the form , namely,

This seems to me to be ill-defined: "a subset of" does not say which subset. From the set builder notation, it looks like this should read "the set of". Am I right? —Quondum 00:52, 5 January 2021 (UTC)[reply]

Not to worry. I have reworded it to be less likely to be misinterpreted. —Quondum 23:10, 6 January 2021 (UTC)[reply]