Talk:Equivalence of Definitions of Associates

The "merge" should be done in the other direction. The definition page needs to be refactored so as to be in the Definition 1 / Definition 2 form (separate transcluded pages), and then this page will itself need to be recrafted so as to be in the format of similar "equivalence of definitions" pages. --prime mover (talk) 11:27, 26 April 2013 (UTC)

Possibly the notation of Definition:Associate/Commutative and Unitary Ring should be changed to $\left({D, +, \circ}\right)$ so this page is consistent? --Linus44 (talk) 23:06, 27 April 2013 (UTC)

Not sure. I'm in two minds about it.

The subtlety is that the third definition is applicable to a CR as well as an ID, the first two only apply to an ID. But in the context of an ID, the third definition is indeed equivalent to the other defs.

As such the transclusion is appropriate, but as "D" is generally used on $\mathsf{Pr} \infty \mathsf{fWiki}$ to denote an integral domain, and "R" a ring, it seems like forcing the pieces to use "D" for that definition for CR.

Perhaps the answer is to split this page into two: one for demonstrating equivalence of 1 and 2 (the existing page, but cut down), and another to show the equivalence of the third definition when applied to an ID, taking special care to explain the applicability of the definitions to the particular objects in question. --prime mover (talk) 23:22, 27 April 2013 (UTC)

Also, there's partial duplication of this result in part (3) of Principal Ideals in Integral Domain. Maybe this should just be added as an "also see" to avoid complications. --Linus44 (talk) 13:29, 10 May 2013 (UTC)