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diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 0b8dc93..71ba622 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -9,12 +9,21 @@
   \usepackage{amsopn}
 \fi
 
+% 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}}}
+
 % 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}}}
+
 % The polynomial ring whose underlying commutative ring of
 % coefficients is the first argument and whose indeterminates (a
 % comma-separated list) are the second argumnt.