Nonabelian or non-abelian?

I asked this question on Mathematics Stack Exchange (here) but I haven’t had any luck so far. Allow me to copy the question:

If I wanted to be scrupulous about correct spelling, is there any reason that I should prefer either:

  • non-abelian or nonabelian?
  • nondegenerate or non-degenerate?
  • hyperkähler or hyper-Kähler?

NB: For some reason, hyperkähler is more common than hyper-Kähler, however quasi-Fuchsian is more common than quasifuchsian, and I don’t think anyone writes “pseudoriemannian”.

While I’m at it, allow me to ask a second spelling question: should I write PDEs or PDE’s? It seems to me that there is no reason to use an apostrophe but a lot of people do.

PS: Wikipedia says something about the use of lowercase “a” in “abelian”: here.

Answer

Three specific answers:

That is what is, but you’re probably asking for what should be. In general though, the orthographic trend is at first for ‘non’ followed by a name-adjective, just like any noun-noun pair, is to go through successive states of neologism:
– ‘non’ followed by a hypen then followed by the capitalized name, eg ‘non-Abelian’
– ‘non’ followed by a hyphen then followed by the uncapitalized name, eg ‘non-abelian’.
– ‘non’ followed directly by the uncapitalized name, eg ‘nonabelian’.

This is because the name part of the word is, at first, very distinctive and meaningful as a name, but slowly becomes opaque, and eventually a regular word, similar genericization, how a trademarked company name, like Kleenex or Google, becomes a corresponding generic, kleenex (for any kind of facial tissue) or google (to search the internet using any search engine).

Attribution
Source : Link , Question Author : Seub , Answer Author : Mitch

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