Covariant functor of soft Γ-hyperrings

Abstract

It is known that a soft [Formula: see text]-hyperring is a generalization of soft ring. The concept of soft [Formula: see text]-hyperring was first introduced by Zhan et al. In fact, Zhan et al. also established three isomorphism theorems of soft rings in 2012. Science then, the study of soft [Formula: see text]-hyperrings has been rapidly grown. The aim of this paper is to consider the equivalence relation on a [Formula: see text]-hyperring previously defined by Zhan et al. It is proved that the above relation is strongly regular and hyperaddition on all quotient soft [Formula: see text]-hyperrings. Also, by using the fundamental relations on [Formula: see text]-hyperrings and hypergroups, we define covariant functor between the category soft [Formula: see text]-hyperrings and soft rings.