777:. One has to infer that they are referring to the same thing, since the linked article does not use or define the notation. A nutshell definition here would be appropriate. Also, one may have a left, right or two-sided principal ideal (all the same for a commutative ring), which is a little confusing given that this article does not firmly commit to being within the framework of commutative rings. It would be nice if it actually defined divisors in the non-commutative context if this use is notable, even if the dominant use might be in the commutative case. —
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is only interesting if it is defined as a divisor of zero with definition (d). It seems to me that we must give weight to more than one definition of divisor, taking care to distinguish (b) and (c). Since (d) seems only to have utility to define a particular useful concept, and this does not seem to
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section then makes statements that are only true with definition (a). In general it seems to me that statements of theorems become more complicated if other than definition (a) is used, but it is not for me to dictate to notable sources. There seems to me to be no utility in excluding zero elements
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technical and deep math theory for something that is an everyday lay-public and school-student idea. It may be true that the (ring theory) article is the fundamental article we currently have on the topic of divisibility, with the ...rules article being an application, but I think having (ring
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as PRIMARYTOPIC, which introduces the idea of what it means to be divisible by something, with then links to the mathmatically technical (ring theory) and the ...rules applications articles.
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That's good point. ("Divisor" in algebraic geometry didn't occur to me when I imported the article from citizendium.) I think what we really need is
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Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a
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I think "Divisibility (ring theory)" is a better title for this article. Otherwise, it sounds like it's about
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It seems clear to me that there are at least two definitions in general notable use, and I'll assume these:
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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This article is self-contradictory, in that it gives a definition equivalent to (b), but the
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be helpful otherwise and I'm guessing is not notable, I'd suggest leaving out this case. —
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Subsequent comments should be made in a new section on this talk page or in a
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are common, but are not included in the definition. This does show up under
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In commutative ring this is not a problem, but otherwise one needs to say "
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Fixing internal inconsistency in article: which definitions are notable?
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Integral domain#Divisibility, prime_elements, and irreducible elements
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Integral domain#Divisibility, prime and irreducible elements
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The above discussion is preserved as an archive of a
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