Theory of hyperrings and hyperfields

descriptionPublicationkeyboard_double_arrow_right Article 01 Nov 1985 English Publisher:Springer Science and Business Media LLCJournal:Algebra and Logic, volume 24, pages 477-485 (issn: 0002-5232, eissn: 1573-8302,

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Authors: Massouros, Ch. G.;

doi: 10.1007/bf01978850

Theory of hyperrings and hyperfields

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Abstract

The notion of hyperfield was introduced by \textit{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.

Keywords

quotient hyperfields, hyperrings, Semirings, Generalizations of fields

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