The McCoy property in Ohm–Rush algebras

An Ohm–Rush algebra $$R \rightarrow S$$ is called McCoy if for any zero-divisor f in S, its content c(f) has nonzero annihilator R, because proved this when $$S=R[x]$$ . We answer a question of Nasehpour by giving class examples faithfully flat algebras with the property that are not weak algebras. However, we show iff $$R/I S/I all radical (resp. prime) ideals I R. When R Noetherian (or more general fidel (A) property), it equivalent S/IS$$ ideals.