\usepackage{amsopn}
\fi
+\input{mjo-common} % for \of, and \binopmany
+
+
+% The direct sum of two things.
+\newcommand*{\directsum}[2]{ {#1}\oplus{#2} }
+
+% The direct sum of three things.
+\newcommand*{\directsumthree}[3]{ \directsum{#1}{\directsum{#2}{#3}} }
+
+% The (indexed) direct sum of many things.
+\newcommand*{\directsummany}[3]{ \binopmany{\bigoplus}{#1}{#2}{#3} }
+
+
% The (sub)algebra generated by its argument, a subset of some ambient
% algebra. By definition this is the smallest subalgebra (of the
% ambient one) containing that set.
\newcommand*{\alg}[1]{\operatorname{alg}\of{{#1}}}
+\ifdefined\newglossaryentry
+ \newglossaryentry{alg}{
+ name={\ensuremath{\alg{X}}},
+ description={the (sub)algebra generated by $X$},
+ sort=a
+ }
+\fi
+
% The fraction field of its argument, an integral domain. The name
% "Frac" was chosen here instead of "Quot" because the latter
% The ideal generated by its argument, a subset consisting of ring or
% algebra elements.
\newcommand*{\ideal}[1]{\operatorname{ideal}\of{{#1}}}
+\ifdefined\newglossaryentry
+ \newglossaryentry{ideal}{
+ name={\ensuremath{\ideal{X}}},
+ description={the ideal generated by $X$},
+ sort=i
+ }
+\fi
+
% The polynomial ring whose underlying commutative ring of
% coefficients is the first argument and whose indeterminates (a