X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-algebra.tex;h=36ad4bd64888c1b2926ff2d454c989e3a561a6aa;hb=2398b156d5cec30d4ede3e65ae1c89ad08551447;hp=59d94874e9a13e38a83bb5274e3c5666fa9e17d3;hpb=85d35b1401a30045cb5b3bca5e8faea5a3248bb3;p=mjotex.git

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 59d9487..36ad4bd 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -9,7 +9,29 @@
   \usepackage{amsopn}
 \fi
 
-\input{mjo-common}
+\input{mjo-common} % for \of, and \binopmany
+
+
+% 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 +69,13 @@
 % 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
 
 
 \fi