mjo-algebra.tex

   1 %
   2 % Abstract algebraic structures.
   3 %
   4 \ifx\havemjoalgebra\undefined
   5 \def\havemjoalgebra{1}
   6
   7
   8 \ifx\operatorname\undefined
   9   \usepackage{amsopn}
  10 \fi
  11
  12 % The (sub)algebra generated by its argument, a subset of some ambient
  13 % algebra. By definition this is the smallest subalgebra (of the
  14 % ambient one) containing that set.
  15 \newcommand*{\alg}[1]{\operatorname{alg}\of{{#1}}}
  16
  17 % The fraction field of its argument, an integral domain. The name
  18 % "Frac" was chosen here instead of "Quot" because the latter
  19 % corresponds to the term "quotient field," which can be mistaken in
  20 % some cases for... a quotient field (something mod something).
  21 \newcommand*{\Frac}[1]{\operatorname{Frac}\of{{#1}}}
  22
  23 % The ideal generated by its argument, a subset consisting of ring or
  24 % algebra elements.
  25 \newcommand*{\ideal}[1]{\operatorname{ideal}\of{{#1}}}
  26
  27 % The polynomial ring whose underlying commutative ring of
  28 % coefficients is the first argument and whose indeterminates (a
  29 % comma-separated list) are the second argumnt.
  30 \newcommand*{\polyring}[2]{{#1}\left[{#2}\right]}
  31
  32
  33 \fi