Results 41 to 50 of about 176 (118)
Journal of HyperstructuresThe purpose of this paper is to introduce and study hyperframes. Where a frame is a generlization of a basis of a vector space, a hyperframe will act as a generalization of a basis in hypervector space.
Cody Cassiday
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Note on Isomorphism Theorems of Hyperrings
International Journal of Mathematics and Mathematical Sciences, Volume 2010, Issue 1, 2010., 2010 There are different notions of hyperrings (R, +, ·). In this paper, we extend the isomorphism theorems to hyperrings, where the additions and the multiplications are hyperoperations.
Muthusamy Velrajan +2 more
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Exact category of hypermodules
International Journal of Mathematics and Mathematical Sciences, Volume 2006, Issue 1, 2006., 2006 It is shown, among other things, that the category of hypermodules is an exact category, thus generalizing the classical case.
A. Madanshekaf
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Hyperfields, truncated DVRs, and valued fields [PDF]
Journal of Number Theory, 2020 For any two complete discrete valued fields $K_1$ and $K_2$ of mixed characteristic with perfect residue fields, we show that if the $n$-th valued hyperfields of $K_1$ and $K_2$ are isomorphic over $p$ for each $n\ge1$, then $K_1$ and $K_2$ are isomorphic.
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New building blocks for F1${\mathbb {F}}_1$‐geometry: Bands and band schemes
Journal of the London Mathematical Society, Volume 111, Issue 4, April 2025.Abstract We develop and study a generalization of commutative rings called bands, along with the corresponding geometric theory of band schemes. Bands generalize both hyperrings, in the sense of Krasner, and partial fields in the sense of Semple and Whittle.
Matthew Baker +2 more
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Field extensions, derivations, and matroids over skew hyperfields [PDF]
, 2018 We show that a field extension $K\subseteq L$ in positive characteristic $p$ and elements $x_e\in L$ for $e\in E$ gives rise to a matroid $M^\sigma$ on ground set $E$ with coefficients in a certain skew hyperfield $L^\sigma$.
Pendavingh, R., Pendavingh, RA Rudi
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Advanced results in enumeration of hyperfields
AIMS Mathematics, 2020 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
R. Ameri, M. Eyvazi, S. Hoskova-Mayerova
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$\lambda$-CONSTACYCLIC CODES OVER FINITE KRASNER HYPERFIELDS
Facta Universitatis, Series: Mathematics and Informatics, 2022 The class of constacyclic codes plays an important role in the theory or error-correcting codes. They are considered as a remarkable generalization of cyclic codes. In this paper, we study constacyclic codes over finite Krasner hyperfields in which we characterize them by their generating polynomial.
Tahan, Madeleine Al, Davvaz, Bijan
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Hyperfields for Tropical Geometry I. Hyperfields and dequantization
, 2010 47 pages, 5 figures, the previous version has been radically changed in order to add new references and correct ...
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OVER THE CONSTRUCTION OF AN HYPERSTRUCTURE OF QUOTIENTS FOR A MULTIPLICATIIVE HYPERRING
Ratio Mathematica, 1997 In this paper we construct a weak hyperfield of quotients for a class of multiplicative hyperrings.
R. Procesi, R. Rota
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