Let R be a chained ring with nilradical N. We prove that R is isonoetherian if and only if R satisfies DCC on annihilators and ACC on infinetly generated ideals if and only if (i) each zero divisor of R is nilpotent, (ii) the module \(N_R\) satisfies DCC on annihilators and ACC on infinitely generated submodules and (iii) R/N is a discrete valuation domain with Krull dimension \(\le 2\) . We show that R satisfies ACC \(_d\) on ideals if and only if R satisfies ACC on infinetly generated ideals if and only if R satisfies epi-ACC on ideals. We study the isonoetherian (respectively satisfies ACC \(_d\) on ideals) property on pseudo-valuation rings and we illustrate results with some examples.
