Results 1 to 10 of about 394 (102)
Methods of constructing hyperfields [PDF]
International Journal of Mathematics and Mathematical Sciences, 1985 In this paper we introduce a class of hyperfields which contains non quotient hyperfields. Thus we give a negative answer to the question of whether every hyperfield is isomorphic to a quotient KG of a field K by some subgroup G of its multiplicative ...
Ch. G. Massouros
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A class of hyperrings and hyperfields [PDF]
International Journal of Mathematics and Mathematical Sciences, 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.
Marc Krasner
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Discussiones Mathematicae - General Algebra and Applications, 2017 In this paper, we define linear codes and cyclic codes over a finite Krasner hyperfield and we characterize these codes by their generator matrices and parity check matrices.
Atamewoue Surdive +3 more
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Recent results in hyperring and hyperfield theory
International Journal of Mathematics and Mathematical Sciences, 1988 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.
Anastase Nakassis
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Characteristic, C-Characteristic and Positive Cones in Hyperfields
Mathematics, 2023 We study the notions of the positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We demonstrate how these interact in order to produce interesting results in the theory of hyperfields.
Dawid Edmund Kędzierski +2 more
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On the Borderline of Fields and Hyperfields
Mathematics, 2023 The hyperfield came into being due to a mathematical necessity that appeared during the study of the valuation theory of the fields by M. Krasner, who also defined the hyperring, which is related to the hyperfield in the same way as the ring is related ...
Christos G. Massouros +1 more
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Matroids over hyperfields [PDF]
AIP Conference Proceedings, 2016 We present an algebraic framework which simultaneously generalizes the notion of linear subspaces, matroids, valuated matroids, and oriented matroids. We call the resulting objects matroids over hyperfields. In fact, there are (at least) two natural notions of matroid in this context, which we call weak and strong matroids.
Baker, Matthew, Bowler, Nathan
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Valuations on Structures More General Than Fields
Computer Sciences & Mathematics Forum, 2023 Valuation theory is an important area of investigation in algebra, with applications in algebraic geometry and number theory. In 1957, M. Krasner introduced hyperfields, which are field-like objects with a multivalued addition, to describe some ...
Alessandro Linzi
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A Result of Krasner in Categorial Form
Mathematics, 2023 In 1957, M. Krasner described a complete valued field (K,v) as the inverse limit of a system of certain structures, called hyperfields, associated with (K,v).
Alessandro Linzi
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ϕ ‐δ‐Primary Hyperideals in Krasner Hyperrings
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this paper, we study commutative Krasner hyperrings with nonzero identity. ϕ‐prime, ϕ‐primary and ϕ‐δ‐primary hyperideals are introduced. The concept of δ‐primary hyperideals is extended to ϕ‐δ‐primary hyperideals. Some characterizations of hyperideals are provided to classify them.
Hao Guan +6 more
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