Implicative Ideal of a Pseudoring

Abstract

In this study, we present the notion of an implicative ideal of a pseudoring and characterize it. We also introduce the notion of a finite product property of a subset of a pseudoring and prove its relations with the implicative and other types of ideal of a pseudoring. Moreover, we demonstrate the relationship between an implicative ideal with prime, polar ideals, as well as the atom of an atomic pseudoring. Finally, we prove that a prime ideal is implicative if and only if it is a maximal ideal of R.