% 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.