\usepackage{amsopn}
\fi
+\input{mjo-common} % for \of, and \binopmany
+
+
+% The multiplicative identity element of its argument, which should be
+% an algebraic structure.
+\newcommand*{\unit}[1]{ 1_{{#1}} }
+
+\ifdefined\newglossaryentry
+ \newglossaryentry{unit}{
+ name={\ensuremath{\unit{R}}},
+ description={the multiplicative identity (unit) element of $R$},
+ sort=u
+ }
+\fi
+
+% 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
% corresponds to the term "quotient field," which can be mistaken in
% some cases for... a quotient field (something mod something).
\newcommand*{\Frac}[1]{\operatorname{Frac}\of{{#1}}}
+% 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
% comma-separated list) are the second argumnt.
\newcommand*{\polyring}[2]{{#1}\left[{#2}\right]}
+\ifdefined\newglossaryentry
+ \newglossaryentry{polyring}{
+ name={\ensuremath{\polyring{R}{X}}},
+ description={polynomials with coefficients in $R$ and variable $X$},
+ sort=p
+ }
+\fi
\fi