The McCoy property in Ohm–Rush algebras

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