If R is a commutative ring .
A is an R - algebra , then A is a finitely presented R - algebra if it is a quotient of a polynomial ring over R in finitely many variables by a finitely generated ideal .
If R is a commutative ring and A is an R - algebra , then A is a finitely presented R - algebra if it is a quotient of a polynomial ring over R in finitely many variables by a finitely generated ideal .