X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-algebra.tex;h=59d94874e9a13e38a83bb5274e3c5666fa9e17d3;hb=6759e3a5bd5fd13bd239ee851c66d1eac83a7c1b;hp=d70d9fd919fa1d39da8036953c03b3d52ce27426;hpb=e157fa83770cf671d8b1ce897964ee5297e0b1eb;p=mjotex.git

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index d70d9fd..59d9487 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -1,5 +1,29 @@
-% Needed for \operatorname.
-\usepackage{amsopn}
+%
+% Abstract algebraic structures.
+%
+\ifx\havemjoalgebra\undefined
+\def\havemjoalgebra{1}
+
+
+\ifx\operatorname\undefined
+  \usepackage{amsopn}
+\fi
+
+\input{mjo-common}
+
+
+% 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
@@ -7,7 +31,22 @@
 % 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]}
+
+
+\fi