\(H_v\)-near rings (Q2709950)

The paper deals with \(H_v\)-structures mainly with \(H_v\)-rings. The notion of \(H_v\)-near rings is introduced, generalizing the notion of hypernear-rings introduced and studied by V. Dašić in 1991. The quotient of a zero-symmetric near-ring with respect to any equivalence relation \((R/\sigma,\oplus,\otimes)\) is considered as a motivating \(H_v\)-near ring. Some results on the introduced \(H_v\)-near rings using \(H_v\)-ideals and strong homomorphisms are obtained. Finally, the fundamental equivalence relation \(\gamma^*\) on \(H_v\)-near rings is defined in a similar way as in the known hyperstructures. Results concerning the fundamental classes and the core \(\omega_R\) of the \(H_v\)-near ring \(R\) are proved.