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

[mjotex.git] / mjo-algebra.tex

diff --git a/mjo-algebra.tex b/mjo-algebra.tex
index d70d9fd919fa1d39da8036953c03b3d52ce27426..71ba6221a1b9f0859fcbcb1530a251f7234e93af 100644 (file)
--- a/mjo-algebra.tex
+++ b/mjo-algebra.tex
@@ -1,5 +1,18 @@
-% Needed for \operatorname.
-\usepackage{amsopn}
+%
+% Abstract algebraic structures.
+%
+\ifx\havemjoalgebra\undefined
+\def\havemjoalgebra{1}
+
+
+\ifx\operatorname\undefined
+  \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
@@ -7,7 +20,14 @@
 % 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.
 \newcommand*{\polyring}[2]{{#1}\left[{#2}\right]}
+
+
+\fi