X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-algebra.tex;h=71ba6221a1b9f0859fcbcb1530a251f7234e93af;hb=17fd11a2ac39c8d20680a61279efed7bd18f93f2;hp=88523456235e4bde91b99d9f99f1fcd41280588c;hpb=fc7cfa7f3d02715cb09eae2e1c6bc501dc2d8d50;p=mjotex.git

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 8852345..71ba622 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -5,8 +5,14 @@
 \def\havemjoalgebra{1}
 
 
-% Needed for \operatorname.
-\usepackage{amsopn}
+\ifx\operatorname\undefined
+  \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
@@ -14,6 +20,10 @@
 % 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.