X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-algebra.tex;h=c4e70c232ba2ccb8ecbc02a5574052e5cd40a895;hb=914fa9f2b50edcf92abfc98c1341e4c9cd6685f5;hp=71ba6221a1b9f0859fcbcb1530a251f7234e93af;hpb=17fd11a2ac39c8d20680a61279efed7bd18f93f2;p=mjotex.git

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 71ba622..c4e70c2 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -9,10 +9,31 @@
   \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
@@ -23,6 +44,14 @@
 % 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