International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 1988 / Article

Open Access

Volume 11 |Article ID 825185 | 12 pages | https://doi.org/10.1155/S0161171288000250

Recent results in hyperring and hyperfield theory

Received01 Dec 1986
Revised30 May 1987

Abstract

This survey article presents some recent results in the theory of hyperfields and hyperrings, algebraic structures for which the “sum” of two elements is a subset of the structure. The results in this paper show that these structures cannot always be embedded in the decomposition of an ordinary structure (ring or field) in equivalence classes and that the structural results for hyperfields and hyperrings cannot be derived from the corresponding results in field and ring theory.

Copyright © 1988 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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