Results 51 to 60 of about 239 (103)

Semiring systems arising from hyperrings [PDF]

, 2022
Hyperfields and systems are two algebraic frameworks which have been developed to provide a unified approach to classical and tropical structures. All hyperfields, and more generally hyperrings, can be represented by systems. Conversely, we show that the
Rowen, Louis, Akian, Marianne, Gaubert, Stephane   +2 more
core   +2 more sources

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, Tong Jin, Oliver Lorscheid   +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, Ameri Reza, Leoreanu-Fotea Violeta   +2 more
doaj   +1 more source

n−ABSORBING I−PRIME HYPERIDEALS IN MULTIPLICATIVE HYPERRINGS [PDF]

Journal of Algebraic Systems
In 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
doaj   +1 more source

Stationary Fourier Hyperfields [PDF]

, 1995
In this paper, we define stationary Fourier hyperfields and prove the structure theorems of stationary Fourier hyperfields.
1722, 60445/profile-ja.html, 30035688, 伊東, 由文, Ito, Yoshifumi, イトウ, ヨシフミ   +5 more
core  

Descartes' rule of signs, Newton polygons, and polynomials over hyperfields [PDF]

, 2022
We develop a theory of multiplicities of roots for polynomials over hyperfields and use this to provide a unified and conceptual proof of both Descartes' rule of signs and Newton's "polygon rule".Comment: 21 pages.
Baker, Matthew, Lorscheid, Oliver
core   +1 more source

Nontrivial solutions for homogeneous linear equations over some non-quotient hyperfields [PDF]

, 2023
We introduce a class of hyperfields which includes several constructions of non-quotient hyperfields. We then use it to partially answer a question posed by M. Baker and T.
Hobby, David, Jun, Jaiung
core   +1 more source

$\lambda$-CONSTACYCLIC CODES OVER FINITE KRASNER HYPERFIELDS

, 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.
Davvaz, Bijan, Al Tahan, Madeleine
core   +1 more source

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
doaj   +1 more source

Universal partial hyperfields of matroids and their prespaces of orderings [PDF]

, 2023
We associate a partial hyperfield ⁽⁰⁾(M) with every matroid M by defining an addition on the elements of its inner Tutte group with an additional zero element such that M is representable over ⁽⁰⁾(M), and every representation of M over a partial ...
Hoya, Marcel
core   +1 more source