\[
\DeclareMathOperator{\End}{End}
\DeclareMathOperator{\char}{char}
\DeclareMathOperator{\tr}{tr}
\DeclareMathOperator{\ker}{ker}
\DeclareMathOperator{\im}{im}
\DeclareMathOperator{\sgn}{sgn}
\DeclareMathOperator{\Hom}{Hom}
\DeclareMathOperator{\span}{span}
\DeclareMathOperator{\diag}{diag}
\DeclareMathOperator{\Id}{Id}
\DeclareMathOperator{\ad}{ad}
\newcommand\d{\mathrm{d}}
\newcommand\pref[1]{(\ref{#1})}
\]

Remark The proof of Proposition 5.3.2 uses the
fact that every finite ring extension is integral. This was not obvious to me
(although I am sure it is obvious to some more sophisticated readers). For the
benefit of the similarly situated, a proof of this fact can be found
here.