Talk:Principal ideal

moved statement

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

The article defines:

• a two-sided principal ideal of $R$ is a subset of all finite sums of elements of the form $ras$, namely, $RaR=\{r_{1}as_{1}+\ldots +r_{n}as_{n}:r_{1},s_{1},\ldots ,r_{n},s_{n}\in R\}.$

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)

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