= Finite-type integer algebra
{title2=$R=\mathbb Z[r_1,\ldots,r_m]$}
= Finitely generated integer algebra
{synonym}
A unital commutative <ring> generated by finitely many elements under addition and multiplication, starting from the image of the integers. Equivalently it is a quotient of a finite-variable <polynomial ring> over $\mathbb Z$. <localization of a ring> at one element remains finite type, since $R[1/r]\cong R[T]/(rT-1)$. Generation here is as an algebra, not merely as a <field extension> when the <ring> happens to be a <field>.
Back to article page
