Talk:Partially ordered ring

Merge proposal

I think that ordered ring should be merged into the "Ordered rings" section of partially-ordered ring because presenting an ordered ring as a partially-ordered ring with an additional property provides the opportunity of gradually building up the topic. The way it currently stands, ordered ring duplicates the definition of a partially-ordered ring, with the additional hypothesis, and it may be unclear to the casual reader how it relates; partially-ordered ring shows the interrelation, and also has a bit more information about ordered rings than the ordered ring article.

« D. Trebbien (talk) 20:03, 30 March 2009 (UTC)

I agree with the proposal. It seems to me that the Ordered Ring article in their definition left something out --- namely, that for ever elt a, either a > 0, or a < 0 or a=0. This is necessary for the order to be total. The PO-ring article has this in it. Justinian11 (talk) 04:32, 1 February 2010 (UTC) Robert Jamison

Question

I hope I am doing this right. I'd like to ask a question and make a comment:

Q) The sets P and S at the beginning of the article are the same. I have called such a set a "positive semiring". Is there a standard name?

C) The notion of "compatible" at the same place should be defined.

Justinian11 (talk) 04:39, 1 February 2010 (UTC)R Jamison

Formalized results

I don't think it's particularly relevant to have a list of results about partially ordered rings formalized in one particular proof assistant, particularly when none of these results are particularly interesting or nontrivial. I've gone ahead and deleted that section, but feel free to revert if you disagree. viiii (talk) 13:26, 26 January 2026 (UTC)