From: Michael Orlitzky <michael@orlitzky.com>
Date: Fri, 1 Nov 2019 21:09:38 +0000 (-0400)
Subject: mjo-algebra: add the \ideal{} generated by a set.
X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=commitdiff_plain;h=42bef52e8272b97d0fae6243dd7621b793086e28

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

diff --git a/examples.tex b/examples.tex
index cb7d28a..af125a7 100644
--- 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 0b8dc93..4f3f79c 100644
--- 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.