The concepts of (semi) hypergroups, hyperrings or hyperfields H differ from the ones of (semi) groups, rings, fields by replacing the operations of addition and multiplication by maps from H×H into the collection of nonempty subsets of H . A hyperring (H,∘,□) is complete if both (H,∘) and (H,□) are complete. The author gives examples for these concepts and relations between them. For instance, each □ -complete hyperfield (H,∘,□) is "integral''; so-called (H,R) -hyperrings, constructed from nonempty, nonintersecting subsets A_i , i∈R , R a ring, are hyperfields if and only if they are fields. Also, left ideals of hyperrings are studied.