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Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sumx+yof two elements,x,y, of a hyperringHis, in general, not an element but a subset ofH. When the non-zero elements of a hyperring form a multiplicative group, the hyperring is called a hyperfield, and this structure generalizes that of a field. A certain class of hyperfields (residual hyperfields of valued fields) has been used by the author  as an importantdoi:10.1155/s0161171283000265 fatcat:hxvj3e5s35gipmqe3sn722yvju