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In this paper we introduce the notion of an $H_v$-near ring
generalizing the notion of a hypernear-ring. We investigate some
properties of $H_v$-near rings and consider the $H_v$-ideals, the
homomorphisms and the factor $H_v$-near rings as well. We also
define the fundamental relation $\gamma^*$ on the $H_v$-near rings
in a similar way in the known hyperstructures and we obtain some
results in this respect.
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