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Recent results in hyperring and hyperfield theory
International Journal of Mathematics and Mathematical Sciences, Volume 11, Issue 2, Page 209-220, 1988., 1987 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 ...
Anastase Nakassis
wiley +1 more source
A class of hyperrings and hyperfields
International Journal of Mathematics and Mathematical Sciences, Volume 6, Issue 2, Page 307-311, 1983., 1983 Hyperring is a structure generalizing that of a ring, but where the addition is not a composition, but a hypercomposition, i.e., the sum x + y of two elements, x, y, of a hyperring H is, in general, not an element but a subset of H. When the non‐zero elements of a hyperring form a multiplicative group, the hyperring is called a hyperfield, and this ...
Marc Krasner
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Some Algebraic Classification of Semiregular Hypermodules in Connection to the Radical
Journal of Mathematics, Volume 2024, Issue 1, 2024.We call a Krasner right S‐hypermodule A regular if each cyclic subhypermodule of A is a direct summand of A, and we also call A semiregular if every finitely generated subhypermodule of A lies above a direct summand of A. In this study, some properties of such hypermodules are achieved.
Yıldız Aydın +2 more
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Quantales and Hyperstructures [PDF]
, 2016 We present a theory of lattice-enriched semirings, called \emph{quantic semirings}, which generalize both quantales and powersets of hyperrings. Using these structures, we show how to recover the spectrum of a Krasner hyperring (and in particular, a ...
Dudzik, Andrew Joseph
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Calculus of meet plus hyperalgebra (tropical semihyperrings)
Communications in Algebra, 2020Bijan Davvaz, M Al Tahan
exaly
Isomorphism Theorems in the Primary Categories of Krasner Hypermodules
Symmetry, 2019Hossein Shojaei, Dario Fasino
exaly
An investigation on ordered algebraic hyperstructures
Acta Mathematica Sinica, English Series, 2017Saber Omidi +2 more
exaly