Set theoretic complete intersection for curves in a smooth affine algebra

Let AA be a regular ring of dimension dd (d≥3d≥3) containing an infinite field kk. Let nn be an integer such that 2n≥d+32n≥d+3. Let II be an ideal in AA of height nn and PP be a projective AA-module of rank nn. Suppose P⊕A≈An+1P⊕A≈An+1 and there is a surjection αα: P→IP→I. It is proved in this note that II is a set theoretic complete intersection ideal. As a consequence, a smooth curve in a smooth affine CC-algebra with trivial conormal bundle is a set theoretic complete intersection if its corresponding class in the Grothendieck group is torsion.