Talk:Q3269789

With or without unit element

@慈居: Integer even numbers form "ring without unit" (there is no item for this), all integer numbers form unital ring (Q3269789). Both these structures are ring (Q161172). So these are 3 different notions. Also there is semiring (Q1333055). For example non-negative integer numbers (with unit) or non-negative integer even numbers (without unit). So these are other 3 types of structures. Please remove "duplicate" statements. Infovarius (talk) 19:11, 31 July 2023 (UTC)

@Infovarius: There is an item for rings "not necessarily" with units – rng (Q17102802) – and I think that's sufficient. 慈居 (talk) 03:56, 1 August 2023 (UTC)

So ring (Q161172)=rng (Q17102802)∪unital ring (Q3269789). --Infovarius (talk) 19:27, 4 August 2023 (UTC)

rng (Q17102802) ∪ unital ring (Q3269789) = rng (Q17102802) (because unital ring (Q3269789) ⊆ rng (Q17102802)), and unital ring (Q3269789) = ring (Q161172)! 慈居 (talk) 03:41, 5 August 2023 (UTC)

And we shouldn't really be confused by those labels. I don't say all use of "ring" is in the sense of "with identity", but it's fine if we have aliases like "ring with identity", etc. 慈居 (talk) 04:15, 5 August 2023 (UTC)

I've created an item for semirings not necessarily with units – hemiring (Q121075789). I don't think it's a good idea to have an item for semirings "without units" also. If so, what about nonassociative ring (Q13512116)? Do you think there should be an "associative ring" and leave it undecided whether a ring (Q161172) is required to be associative? 慈居 (talk) 04:59, 1 August 2023 (UTC)

The answer for your last question is "yes". We don't need items for something that "not necessary" has some property. I.e. if we has class A and its subclass B (which are "all As which has property P"), then we don't generally need item "all As which don't necessary have P" - this is even not "A\B", this is simply A! So your hemiring (Q121075789) seems to be equivalent to semiring (Q1333055). --Infovarius (talk) 19:27, 4 August 2023 (UTC)

@Infovarius: I completely agree that "we don't generally need item 'all As which don't necessary have P'". Actually hemiring (Q121075789) is what you describe as "Class A", and semiring (Q1333055) "Class B". Property P is then "with identity". I describe "hemiring" as "semiring but not necessarily with identity" because that's how people normally describe it. Note also that semirings and hemirings are used in this sense in https://doi.org/10.1007/978-94-015-9333-5; I didn't choose the terms arbitrarily.

Class A	Property P	Class B
rng (Q17102802)	with identity	ring (Q161172) (= unital ring (Q3269789))
hemiring (Q121075789)	with identity	semiring (Q1333055)

I'm opposed to make ring (Q161172) just an ambiguous terminology. Ring (Q534381) will suffice for this purpose. I've already checked (when I mark unital ring (Q3269789) as duplicate) that all "instance of"/"subclass of":ring (Q161172) statements are best interpreted as "instance of"/"subclass of":"associative ring with identity". 慈居 (talk) 04:09, 5 August 2023 (UTC)

I know there are some articles in English Wikipedia covering all senses of a single math terminology. But that's not widely accepted in other local Wikimedia projects (such as Korean Wikipedia, etc.) and w:Ring (mathematics) is even not such an article – rings are clearly defined to have a multiplicative monoid, not just a semigroup, nor does it ambiguate the term. 慈居 (talk) 04:31, 5 August 2023 (UTC)

@Toni 001: Regarding whether ring (Q161172) is for rings with identity we've already had discussion here. What's your thought on it? 慈居 (talk) 08:41, 16 August 2023 (UTC)