Why \allowbreak is not working?

This is another case for which \left and \right are not appropriate:

1. there is no delimiter to increase the size of;

2. the spaces after commas cannot participate to stretching or shrinking together with the other spaces in the same line;

3. the formula is not breakable across lines under any circumstance.

So the first step to do is to remove \left and \right (and to disable any automatic feature in the editor). Then a carefully placed \linebreak[0] will help in the pagination.

\documentclass[a4paper]{article}
\usepackage{amsfonts,amsthm}
\newtheorem{theorem}{Theorem}


\begin{document}

\noindent\parbox{4cm}{
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \langle
  \mathbb{S},\mathbb{E},f,
  \mathbb{V},\mathbb{R},\mathbb{C},\linebreak[0]
  Op_a,Op_c,Op_m \rangle$.
\end{theorem}
}

\noindent\parbox{6.5cm}{
\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \langle
  \mathbb{S},\mathbb{E},f,\linebreak[0]
  \mathbb{V},\mathbb{R},\mathbb{C},
  Op_a,Op_c,Op_m \rangle$.
\end{theorem}
}

\begin{theorem}
...could be now considered as an algebraic structure $DB_E = \langle
  \mathbb{S},\mathbb{E},\linebreak[0]
  f,\mathbb{V},\mathbb{R},\mathbb{C},
  Op_a,Op_c,Op_m \rangle$.
\end{theorem}

\end{document}