- If $R$ is a \index{commutative ring}, then $\polyring{R}{X,Y,Z}$
- is a multivariate polynomial ring with indeterminates $X$, $Y$,
- and $Z$, and coefficients in $R$. If $R$ is a moreover an integral
- domain, then its fraction field is $\Frac{R}$.
+ If $R$ is a commutative ring\index{commutative ring}, then
+ $\polyring{R}{X,Y,Z}$ is a multivariate polynomial ring with
+ indeterminates $X$, $Y$, and $Z$, and coefficients in $R$. If $R$
+ is a moreover an integral domain, then its fraction field is
+ $\Frac{R}$. If $x,y,z \in R$, then $\ideal{\set{x,y,z}}$ is the
+ ideal generated by $\set{x,y,z}$, which is defined to be the
+ smallest ideal in $R$ containing that set. Likewise, if we are in
+ an algebra $\mathcal{A}$ and if $x,y,z \in \mathcal{A}$, then
+ $\alg{\set{x,y,z}}$ is the smallest subalgebra of $\mathcal{A}$
+ containing the set $\set{x,y,z}$.
+
+ If $R$ has a multiplicative identity (that is, a unit) element,
+ then that element is denoted by $\unit{R}$. Its additive identity
+ element is $\zero{R}$. The stabilizer (or isotropy)
+ subgroup of $G$ that fixes $x$ is $\Stab{G}{x}$.
+
+ If $I$ is an ideal, then $\variety{I}$ is the variety that
+ corresponds to it.