2 % Abstract algebraic structures.
4 \ifx\havemjoalgebra\undefined
8 \ifx\operatorname\undefined
15 % The (sub)algebra generated by its argument, a subset of some ambient
16 % algebra. By definition this is the smallest subalgebra (of the
17 % ambient one) containing that set.
18 \newcommand*
{\alg}[1]{\operatorname{alg
}\of{{#1}}}
19 \ifdefined\newglossaryentry
20 \newglossaryentry{alg
}{
21 name=
{\ensuremath{\alg{X
}}},
22 description=
{the (sub)algebra generated by $X$
},
28 % The fraction field of its argument, an integral domain. The name
29 % "Frac" was chosen here instead of "Quot" because the latter
30 % corresponds to the term "quotient field," which can be mistaken in
31 % some cases for... a quotient field (something mod something).
32 \newcommand*
{\Frac}[1]{\operatorname{Frac
}\of{{#1}}}
34 % The ideal generated by its argument, a subset consisting of ring or
36 \newcommand*
{\ideal}[1]{\operatorname{ideal
}\of{{#1}}}
37 \ifdefined\newglossaryentry
38 \newglossaryentry{ideal
}{
39 name=
{\ensuremath{\ideal{X
}}},
40 description=
{the ideal generated by $X$
},
46 % The polynomial ring whose underlying commutative ring of
47 % coefficients is the first argument and whose indeterminates (a
48 % comma-separated list) are the second argumnt.
49 \newcommand*
{\polyring}[2]{{#1}\left[{#2}\right]}