X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-algebra.tex;h=25b96d9f8a184edc051ed2867bc8fa9b4b0a269b;hp=36ad4bd64888c1b2926ff2d454c989e3a561a6aa;hb=HEAD;hpb=f82e8e51ac99547bab1a02d678a1476971f17444

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 36ad4bd..3bb51c1 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -12,6 +12,18 @@
 \input{mjo-common} % for \of, and \binopmany
 
 
+% The additive identity element of its argument, which should be
+% an algebraic structure.
+\newcommand*{\zero}[1]{ 0_{{#1}} }
+
+\ifdefined\newglossaryentry
+  \newglossaryentry{zero}{
+    name={\ensuremath{\zero{R}}},
+    description={the additive identity element of $R$},
+    sort=z
+  }
+\fi
+
 % The multiplicative identity element of its argument, which should be
 % an algebraic structure.
 \newcommand*{\unit}[1]{ 1_{{#1}} }
@@ -78,4 +90,21 @@
 \fi
 
 
+% The stabilizer subgroup of its first argument that fixes the point
+% given by its second argument.
+\newcommand*{\Stab}[2]{ #1_{#2} }
+
+
+% The affine algebraic variety consisting of the common solutions to
+% every polynomial in its argument, which should be a subset of some
+% polynomial ring.
+\newcommand*{\variety}[1]{ \mathcal{V}\of{{#1}} }
+\ifdefined\newglossaryentry
+  \newglossaryentry{variety}{
+    name={\ensuremath{\variety{I}}},
+    description={variety corresponding to the ideal $I$},
+    sort=v
+  }
+\fi
+
 \fi