# a thinner “ring of integers” $\mathcal{O}$

Throughout Neukirch's Algebraic Number Theory, he denotes Dedekind domains and their extension respectively with a small and a large version of what I can only describe as a thinner (i.e., less bolded) $\mathcal{O}$, which is commonly used symbol to denote the ring of integers of a number field.

Here is a usage in the book where it is side by side with the standard $\mathcal{O}$:

How can I reproduce these symbols? They don't appear to be in the standard alphabets (like \mathcal, \mathfrak, etc.).

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On TeX.SE, visualization of TeX is usually done through an image upload, rather than a rendering via MathJax, say. I've removed that from your post since most people know this. See Why doesn't maths render as maths? –  Werner Jun 25 '12 at 0:49
For symbol lookup or identification, see How to look up a symbol? Are you able to find your symbol using any of the methods described in the linked post? Give some feedback. –  Werner Jun 25 '12 at 0:52
@Werner: No, it's not in the "Comprehensive LaTeX symbols" link and detexify-ing just gave me $\mathcal{O}$. –  JSeaton Jun 25 '12 at 1:07
@Werner: is there a place where I can see the alphabet rendered into the different math fonts? I'm willing to be that this is symbol is just the letter 'o' in some particular math font. –  JSeaton Jun 25 '12 at 1:09
See the mathalfa package (ctan.org/tex-archive/macros/latex/contrib/mathalfa) for an overview of math alphabets. –  Mico Jun 25 '12 at 1:37

This looks like a resized \mathcal{O} to \scriptsize:

\documentclass{article}
\newcommand{\dedekind}{{$\scriptstyle\mathcal{O}$}}
\begin{document}
\noindent \textbf{(8.1) Proposition.} \slshape Let~\dedekind\ be a Dedekind domain
with field of fractions~$K$, let $L|K$ be a finite extension of~$K$ and~$\mathcal{O}$
the integral closure of~\dedekind\ in~$L$. Then~$\mathcal{O}$ is again a Dedekind
domain.
\end{document}


Depending on the usage (commonly standalone or part of math expressions), the following definition might be of benefit:

\newcommand{\dedekind}{\ensuremath{\scriptstyle\mathcal{O}}}


\ensuremath allows you to intermix the usage within math and text mode. A more extensive definition of \dedekind would include \mathchoice to allow for resizing of \mathcal{O} "dynamically" if used in superscript.

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Thank you for the great response. –  JSeaton Jun 25 '12 at 3:20
It's also nice to see more examples of where ties are supposed to be used. I can never figure it out myself. –  Ryan Reich Jun 25 '12 at 4:11