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.

Hyperrings and hyperfields

DE SALVO, Mario
1984-01-01

Abstract

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.
1984
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11570/2089623
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