Results 21 to 30 of about 239 (103)
AIMS Mathematics127 pages, 305 tables Subj-class: math.RA - Rings and Algebras MSC-class: 16Y20 (Primary); 20N20 (Secondary) We extend the results of our previous papers and we reduce the axioms of the definition of the hyperfield. This facilitates the construction, enumeration and classification of all the hyperfields of order 7, while also revealing an important ...
Christos Massouros +1 more
exaly +3 more sources
THE CLASS OF KRASNER HYPERFIELDS IS NOT ELEMENTARY [PDF]
The Journal of Symbolic LogicAbstract We show that the class of Krasner hyperfields is not elementary. To show this, we determine the rational rank of quotients of multiplicative groups in field extensions. We also discuss some related questions.
Błaszkiewicz, Piotr, Kowalski, Piotr
core +4 more sources
Small weak hyperfields in hadronic mechanics
Ratio MathematicaIt was in mid 90es when Professor R. M. Santilli realized, for the first time, that his innovating theories can be appropriate expressed by multi-valued systems.
Thomas Vougiouklis
doaj +2 more sources
On the hyperfields associated to valued fields
Journal of Pure and Applied AlgebraOne can associate to a valued field an inverse system of valued hyperfields $(\mathcal{H}_i)_{i \in I}$ in a natural way. We investigate when, conversely, such a system arise from a valued field. First, we extend a result of Krasner by showing that the inverse limit of certain systems are stringent valued hyperfields.
Alessandro Linzi, Pierre Touchard
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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ϕ ‐δ‐Primary Hyperideals in Krasner Hyperrings
Mathematical Problems in Engineering, Volume 2022, Issue 1, 2022., 2022 In this paper, we study commutative Krasner hyperrings with nonzero identity. ϕ‐prime, ϕ‐primary and ϕ‐δ‐primary hyperideals are introduced. The concept of δ‐primary hyperideals is extended to ϕ‐δ‐primary hyperideals. Some characterizations of hyperideals are provided to classify them.
Hao Guan +6 more
wiley +1 more source
On 1‐Absorbing Prime Hyperideal and Some of Its Generalizations
Journal of Mathematics, Volume 2022, Issue 1, 2022., 2022 In this paper, we introduce the concept of 1‐absorbing prime hyperideals which is an expansion of the prime hyperideals. Several properties of the hyperideals are provided. For example, it is proved that if a strong C‐hyperideal I of R is 1‐absorbing prime that is not prime, then R is a local multiplicative hyperring.
M. Anbarloei +1 more
wiley +1 more source
[Retracted] Roughness in Hypervector Spaces
Journal of Function Spaces, Volume 2022, Issue 1, 2022., 2022 This paper examines rough sets in hypervector spaces and provides a few examples and results in this regard. We also investigate the congruence relations‐based unification of rough set theory in hypervector spaces. We introduce the concepts of lower and upper approximations in hypervector spaces.
Nabilah Abughazalah +3 more
wiley +1 more source
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
doaj +1 more source