X-Git-Url: http://gitweb.michael.orlitzky.com/?a=blobdiff_plain;f=mjo-algebra.tex;h=59d94874e9a13e38a83bb5274e3c5666fa9e17d3;hb=6759e3a5bd5fd13bd239ee851c66d1eac83a7c1b;hp=0b8dc93c2df8ad9da5f2b911c61eb251bc8f6b43;hpb=e6bb4f9ae2d3785b331388703b8793e0409d30af;p=mjotex.git

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 0b8dc93..59d9487 100644
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -9,12 +9,40 @@
   \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
 % corresponds to the term "quotient field," which can be mistaken in
 % 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.