mjo-algebra: add \alg{} for the subalgebra generated by a set.

diff --git a/examples.tex b/examples.tex
index af125a726265dbfd53b150bc42cca2cfeb5c3c6f..c00279b16beb44514ae8e80e371d8dc3f8392a35 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -30,8 +30,12 @@
     is a multivariate polynomial ring with indeterminates $X$, $Y$,
     and $Z$, and coefficients in $R$. If $R$ is a moreover an integral
     domain, then its fraction field is $\Frac{R}$. If $x,y,z \in R$,
-    then $\ideal{\set{x,y,z}}$ is the ideal generated by $\set{x,y,z}$,
-    which is defined to be the smallest ideal in $R$ containing that set.
+    then $\ideal{\set{x,y,z}}$ is the ideal generated by
+    $\set{x,y,z}$, which is defined to be the smallest ideal in $R$
+    containing that set. Likewise, if we are in an algebra
+    $\mathcal{A}$ and if $x,y,z \in \mathcal{A}$, then
+    $\alg{\set{x,y,z}}$ is the smallest subalgebra of $\mathcal{A}$
+    containing the set $\set{x,y,z}$.
   \end{section}
 
   \begin{section}{Algorithm}

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 4f3f79cd5dab03694d66be516bb4b157c7c1e1c9..71ba6221a1b9f0859fcbcb1530a251f7234e93af 100644 (file)
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -9,6 +9,11 @@
   \usepackage{amsopn}
 \fi
 
+% 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}}}
+
 % 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