Two New Types of Rings Defined by Using a Translational Invariant Fuzzy Subset

Abstract

We use a translational invariant fuzzy subset 𝑝 of a ring 𝑅 to define two new types of commutative rings namely, 𝑝-presimplifiable and 𝑝-associate rings. We present some results of these rings. The interest of these results is that most of them are mirrors of corresponding results of presimplifiable and associate rings in classical ring theory.