Definition talk:Prime Ideal of Ring/Commutative and Unitary Ring

"Can we change the assumption Definition:Commutative and Unitary Ring to Definition:Commutative Ring? The unused unitary assumption makes these definitions less applicable."


 * My immediate response would be: No, because a specific effort was made by a contributor to define this concept specifically for a commutative and unitary ring. I don't know what that specific reason was, he did not share his unsourced, uncorroborated and somewhat scattergun agenda. I am reluctant to throw that all away because there's no immediate vision of where this was going.


 * There is already a definition for the general ring. Are you able to just use that? If you do need to use a definition specifically for a general commutative ring (which may or may not be unitary), then feel free to add another subpage to the existing structure, and if it turns out that we really do not need the Commutative and Unitary Ring version, we can subsequently remove it without compromising the validity of anything. --prime mover (talk) 14:39, 1 July 2022 (UTC)


 * I need the equivalence of Definition1, Definition2 and Definition3. Its proof does not require the unity at all. The same holds for many subsequent results, too. Ultimately, we should remove the with unity-assumption, where it is unnecessary.
 * I guess the reason for this unnecessary assumption is simply that many books on commutative algebra (e.g. Atiyah & MacDonald) generally defines the ring as with unity.
 * I must wait a bit. No idea what to do. --Usagiop (talk) 16:32, 1 July 2022 (UTC)


 * The best approach to populating this site is to pick a source work and go over it in rigorous detail. At the least, every definition should be documented and compared with existing definitions, and merging as appropriate. It takes considerable critical thinking skills and attention to detail. Unfortunately this can be tedious and time-consuming.


 * The danger is always that one source work takes a subtly different approach from another, and if you take a result from one work and refer back to definitions sourced from a different work, you can find the differences are significant. Hence our rigorous attention to detail and a rigid approach to the source flow.


 * But of course you know and understand all this, because you have read the help pages and thoroughly understand our site philosophy. --prime mover (talk) 18:44, 1 July 2022 (UTC)