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Theory of hyperrings and hyperfields. (English) Zbl 0615.16027

Algebra Logic 24, 477-485 (1985); reprint from Algebra Logika 24, No. 6, 728-742 (1985).
The notion of hyperfield was introduced by M. Krasner [Colloq. d’Algèbre Supérieure, CBRM, Bruxelles 1956, 129-206 (1959; Zbl 0085.265)] who raised the following question: Are all hyperfields isomorphic to quotient hyperfields? He also raised an analogous question for hyperrings. The author gives constructions of hyperfields and hyperrings, which prove that there are non quotient hyperfields and hyperrings.
Reviewer: S.M.Yusuf

MSC:

16Y60 Semirings
12K99 Generalizations of fields

Citations:

Zbl 0085.265
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References:

[1] M. Krasner, ”Approximation des corps valués complets de caractéristique p par ceux de caractéristique O,” Colloque d’Algèbre Superieure (Bruxelles, Décembre 1956), CBRM, Bruxelles (1957).
[2] M. Krasner, ”Espaces ultramétriqueset nombres semi-réels,” C.R. Acad. Sci.,219, (1944). · Zbl 0061.06202
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[10] D. Stratigopoulos, ”Hyperanneaus non commutatifs: le radical d’un hyperanneasu, somme sous-directe des hyperanneaux, hyperanneaux artiniens et théorie des elements idempotents,” C.R. Acad. Sci.,A269, 627–629 (1969). · Zbl 0199.35001
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[13] D. Stratigopoulos and Ch. G. Massouros, ”On a class of fields,” Math. Balkanica,12 (to appear).
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