International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 2, Pages 209-220

Recent results in hyperring and hyperfield theory

Anastase Nakassis

9 Keystone Court, Gaithersburg, MD 20878, USA

Received 1 December 1986; Revised 30 May 1987

Copyright © 1988 Anastase Nakassis. 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.


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.