Results 1 to 10 of about 47 (45)
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
exaly +3 more sources
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 Kedzierski +2 more
exaly +3 more sources
Quadratic structures associated to (multi)rings [PDF]
Categories and General Algebraic Structures with Applications, 2022 We consider certain pairs (A, T) where A is a (multi)ring andT ⊆ A is a multiplicative set that generates, by a convenient quotient construction,a (multi)structure that supports a quadratic form theory: withsome natural hypotheses we generalize ...
Kaique Roberto +2 more
doaj +1 more source
K-theories and Free Inductive Graded Rings in Abstract Quadratic Forms Theories [PDF]
Categories and General Algebraic Structures with Applications, 2022 We build on previous work on multirings ([17]) that providesgeneralizations of the available abstract quadratic forms theories (specialgroups and real semigroups) to the context of multirings ([10], [14]).
Kaique Roberto, Hugo Mariano
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Existence theorem of finite krasner hyperfields [PDF]
Journal of Hyperstructures, 2021 The concern of this paper is to show that there always exist Krasner hyperfields of order n, where n is an integer greaterthan or equal to 2.
Yuming Feng +3 more
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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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Methods of constructing hyperfields
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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Hyperstructures in Lie-Santilli Admissibility and Iso-Theories
Ratio Mathematica, 2017 In the quiver of hyperstructures Professor R. M. Santilli, in early 90'es, tried to find algebraic structures in order to express his pioneer Lie-Santilli's Theory.
Maria Santilli Ruggero +1 more
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Root Selections and 2p-th Root Selections in Hyperfields
Discussiones Mathematicae - General Algebra and Applications, 2019 In this paper we define root selections and 2p-th root selections for hyperfields: these are multiplicative subgroups whose existence is equivalent to the existence of a well behaved square root function and 2p-th root function, respectively.
Gładki Paweł
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