mjo-algebra: add the \ideal{} generated by a set.

diff --git a/examples.tex b/examples.tex
index cb7d28a1f41d3a17c02635b370c3cb0fbe36a54f..af125a726265dbfd53b150bc42cca2cfeb5c3c6f 100644 (file)
--- a/examples.tex
+++ b/examples.tex
@@ -29,7 +29,9 @@
     If $R$ is a \index{commutative ring}, then $\polyring{R}{X,Y,Z}$
     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 $\Frac{R}$.
+    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.
   \end{section}
 
   \begin{section}{Algorithm}

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index 0b8dc93c2df8ad9da5f2b911c61eb251bc8f6b43..4f3f79cd5dab03694d66be516bb4b157c7c1e1c9 100644 (file)
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -15,6 +15,10 @@
 % 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}}}
+
 % The polynomial ring whose underlying commutative ring of
 % coefficients is the first argument and whose indeterminates (a
 % comma-separated list) are the second argumnt.