Talk:Complement of Prime Ideal of Ring is Multiplicatively Closed

Not to merge to Definition of prime ideal

This theorem is not the same as Definition:Prime Ideal of Commutative and Unitary Ring/Definition 3.

Definition:Multiplicatively Closed Subset of Ring is another concept.--Usagiop (talk) 09:38, 27 September 2022 (UTC)

So you're perfectly okay with having needless repetition between two pages? --prime mover (talk) 16:56, 27 September 2022 (UTC)

This is not a repetition, it is rather a coincidence that these two different concepts are equivalent in this specific case. The mutiplicatively closedness is a key concept in localization theory, that is primarily nothing to do with ideals. Then, the localization at (the complement of) a prime ideal is presumably the most important example of localization. This theorem is needed as a step to show such relations. --Usagiop (talk) 18:51, 27 September 2022 (UTC)