Results 31 to 40 of about 112 (84)
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
wiley +1 more source
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
wiley +1 more source
Commutative hypergroups associated with a hyperfield [PDF]
Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2017 Let [Formula: see text] be a commutative hypergroup and [Formula: see text] a discrete commutative hypergroup. In this paper we introduce a commutative hypergroup [Formula: see text] associated with a hyperfield [Formula: see text] of [Formula: see text] based on [Formula: see text].
Heyer, Herbert +3 more
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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
wiley +1 more source
Normal hyperideals in Krasner (m, n)-hyperrings
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2018 Using a new definition, with respect to [21], for normal hyperideals in Krasner (m, n)-hyperrings, we show that the corresponding quotient structures are (m, n)-rings.
Norouzi Morteza +2 more
doaj +1 more source
n−ABSORBING I−PRIME HYPERIDEALS IN MULTIPLICATIVE HYPERRINGS [PDF]
Journal of Algebraic SystemsIn this paper, we define the concept $I-$prime hyperideal in a multiplicative hyperring $R$. A proper hyperideal $P$ of $R$ is an $I-$prime hyperideal if for $a, b \in R$ with $ab \subseteq P-IP$ implies $a \in P$ or $b \in P$.
Ali Abdullah Mena, Ismael Akray
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Fundamental relation on m-idempotent hyperrings
Open Mathematics, 2017 The γ*-relation defined on a general hyperring R is the smallest strongly regular relation such that the quotient R/γ* is a ring. In this note we consider a particular class of hyperrings, where we define a new equivalence, called εm∗$\varepsilon^{*}_{m}
Norouzi Morteza, Cristea Irina
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Geometry of tropical extensions of hyperfields [PDF]
Proceedings of the Royal Society of Edinburgh: Section A MathematicsWe study the geometry of tropical extensions of hyperfields, including the ordinary, signed, and complex tropical hyperfields. We introduce the framework of ‘enriched valuations’ as hyperfield homomorphisms to tropical extensions and show that a notable family of them are relatively algebraically closed.
James Maxwell, Ben Smith
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$\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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