let k be a field, k[a] algebric extension. if A is reduced commutative algebra over K[a] and B is subring which is algebra over k. then if there exits elements $x,y\in A$ such that $xa+y=0$, then: x=y=0.

if it is not true in the general case, is it true in the case where: k[a] is inseparable extension of degree p over k , A is finitely generated, and $B=A^{p}=\{{y^{p}\,|\, y\in A\}}$