X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-algebra.tex;h=25b96d9f8a184edc051ed2867bc8fa9b4b0a269b;hp=fb930279e46e851855845e6e32820e9504ec20a8;hb=HEAD;hpb=0764c4b643f444e4e46c6b3481ba32962bee5bfe

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index fb93027..3bb51c1 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -9,7 +9,41 @@
   \usepackage{amsopn}
 \fi
 
-\input{mjo-common} % for \of, at least
+\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}} }
+
+\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
@@ -47,6 +81,30 @@
 % 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
+
 
+% 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