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\documentclass[a4paper,10pt]{scrartcl}
\usepackage[latin1]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{amsmath}
\DeclareMathOperator{\Erdoel}{\textrm{Erdöl}}
\DeclareMathOperator{\Erdoelddot}{Erd\ddot{o}l}
\begin{document}
$\Erdoel \Erdoelddot$
\end{document}