X-Git-Url: http://gitweb.michael.orlitzky.com/?p=mjotex.git;a=blobdiff_plain;f=mjo-algebra.tex;fp=mjo-algebra.tex;h=59d94874e9a13e38a83bb5274e3c5666fa9e17d3;hp=71ba6221a1b9f0859fcbcb1530a251f7234e93af;hb=85d35b1401a30045cb5b3bca5e8faea5a3248bb3;hpb=17fd11a2ac39c8d20680a61279efed7bd18f93f2 diff --git a/mjo-algebra.tex b/mjo-algebra.tex index 71ba622..59d9487 100644 --- a/mjo-algebra.tex +++ b/mjo-algebra.tex @@ -9,10 +9,21 @@ \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 @@ -23,6 +34,14 @@ % 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