Results 1 to 10 of about 112 (84)
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 Massouros +1 more
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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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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 Kedzierski +2 more
exaly +5 more sources
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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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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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
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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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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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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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Witt rings of quadratically presentable fields [PDF]
Categories and General Algebraic Structures with Applications, 2020 This paper introduces an approach to the axiomatic theory of quadratic forms based on {tmem{presentable}} partially ordered sets, that is partially ordered sets subject to additional conditions which amount to a strong form of local presentability.
Pawel Gladki, Krzysztof Worytkiewicz
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