X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-algebra.tex;h=36ad4bd64888c1b2926ff2d454c989e3a561a6aa;hb=7dfe6fdee9d819258393544917c871f6b85a3eb8;hp=88523456235e4bde91b99d9f99f1fcd41280588c;hpb=fc7cfa7f3d02715cb09eae2e1c6bc501dc2d8d50;p=mjotex.git

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 8852345..36ad4bd 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -5,8 +5,47 @@
 \def\havemjoalgebra{1}
 
 
-% Needed for \operatorname.
-\usepackage{amsopn}
+\ifx\operatorname\undefined
+  \usepackage{amsopn}
+\fi
+
+\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
+% 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
@@ -14,10 +53,29 @@
 % 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}}}
+\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
 % 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