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The context is algebraic number theory.

How to pronounce the symbols $\mathcal{O}_K$ (ring of integers in $K$) and $\mathfrak{m}_K$ (maximal ideal) ?

How to pronounce $\mathcal{O}_K^n$ ?

Note \mathcal{O}_K for $\mathcal{O}_K$ and \mathfrak{m}_K for $\mathfrak{m}_K$.

There is book has some clue.

So I am thinking the following pronunciations:

$\mathcal{O}_K \xrightarrow{pronunciation} O~\text{subscript}~K$

$\mathcal{O}_K^n \xrightarrow{pronunciation} O~\text{subscript}~K~\text{to the}~n~\text{power},~~\text{Or,}~O~\text{subscript}~K~\text{raised to the}~n$

$\mathfrak{m}_K \xrightarrow{pronunciation} m~\text{subscript}~K$.

Is it enough ?

MAS
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    I would just say oh-sub-kay, oh-sub-kay-to-the-en, em-sub-kay. – Gerry Myerson Jun 17 '22 at 05:14
  • @GerryMyerson, thanks. So use sub instead of subscript – MAS Jun 17 '22 at 05:16
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    Nothing wrong with "subscript", I'm just telling you what I would say, not that other options are wrong. – Gerry Myerson Jun 17 '22 at 05:17
  • @GerryMyerson, I understand 'to save energy' – MAS Jun 17 '22 at 05:17
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    I call these 'Oh Kay en,' don't feel the need to include the details of "sub" and such. Also in algebraic geometry, this is the structure sheaf, and I'm pretty sure that this notation is not an accident. In a suitably general setting, you could probably just call it "the structure sheaf." – A. Thomas Yerger Jun 17 '22 at 05:34
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    If the $n$ in $K^n$ is not an exponent, say "kay sup n". Now does anyone know how to pronounce $\sinh x$? – DanielWainfleet Jun 17 '22 at 05:35
  • @DanielWainfleet, thanks. May be $sinh~x$ should enhance the hyperbolic property of $sin~x$ here. Say, sin hyperbolic x or hyperbolic sin x. What do we pronounce for $h_H$ ? Is the pronunciation h sub capital H alright ? – MAS Jun 17 '22 at 10:36
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    @DanielWainfleet see https://math.stackexchange.com/a/176070/26369 for hyperbolic trig pronunciations – Mark S. Jun 17 '22 at 12:20
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    MAI, to save energy is one thing, but for several people it helped to know that $\mathcal{O}$ is not "Oh" but rather "calligraphic Oh". Of course you would skip this afterwards then. Actually, see here for the notion. – Dietrich Burde Jun 18 '22 at 08:34
  • @DietrichBurde, so you suggest to pronounce calligraphic Oh for $\mathcal{O}$. Is it ? Actually I read some slide in a conference – MAS Jun 18 '22 at 14:05
  • @DietrichBurde, how to pronounce $\mathcal{C}$ for any cap letter ? Here \mathcal{C} for $\mathcal{C}$. Should I say script C or caligraphic C ? – MAS Jun 22 '22 at 03:36

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