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: 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)
 * a two-sided principal ideal of $$R$$ is a subset of all finite sums of elements of the form $$ras$$, namely, $$RaR = \{r_1 a s_1 + \ldots + r_n a s_n: r_1,s_1, \ldots, r_n, s_n \in R\}.$$
 * Not to worry. I have reworded it to be less likely to be misinterpreted.  —Quondum 23:10, 6 January 2021 (UTC)