Zobrazeno 1 - 9
of 9
pro vyhledávání: '"Alessandro Linzi"'
Autor:
Alessandro Linzi
Publikováno v:
AIMS Mathematics, Vol 9, Iss 5, Pp 11247-11277 (2024)
We express the fundamental properties of commutative polygroups (also known as canonical hypergroups) in category-theoretic terms, over the category $ \mathbf{Set} $ formed by sets and functions. For this, we employ regularity as well as the monoidal
Externí odkaz:
https://doaj.org/article/88d9858748b94e92bb1882c0c5378db0
Autor:
Alessandro Linzi
Publikováno v:
Mathematics, Vol 11, Iss 24, p 4923 (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). We put this result in purely category-theoretic terms by translating it into a limit constr
Externí odkaz:
https://doaj.org/article/03c8c59af6d544b5ae626fca66ae2cae
Autor:
Alessandro Linzi
Publikováno v:
Computer Sciences & Mathematics Forum, Vol 7, Iss 1, p 2 (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 struc
Externí odkaz:
https://doaj.org/article/18e17013f78748f0b2e6888db23d22ed
Publikováno v:
Mathematics, Vol 11, Iss 3, p 779 (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. For instance, we provide a criterion for
Externí odkaz:
https://doaj.org/article/7189ec58af4946e9b0bcf46b573a4877
Autor:
Alessandro Linzi, Irina Cristea
Publikováno v:
Symmetry, Vol 15, Iss 2, p 311 (2023)
With the aim of developing the recent theory of dependence relations, we elaborate a procedure to measure the strength of the influence of an element on another with respect to a given dependence relation on a finite set. We call this measure the deg
Externí odkaz:
https://doaj.org/article/2c382a1acd5645628e43883041a78207
Publikováno v:
Journal of Algebra. 611:399-421
We introduce and study in detail the notion of compatibility between valuations and orderings in real hyperfields. We investigate their relation with valuations and orderings induced on factor and residue hyperfields. Much of the theory from real fie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::c4d363da89e95d656efaae003d92b7be
https://doi.org/10.1016/j.jalgebra.2022.08.006
https://doi.org/10.1016/j.jalgebra.2022.08.006
Publikováno v:
Mathematics
Volume 11
Issue 3
Pages: 779
Volume 11
Issue 3
Pages: 779
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. For instance, we provide a criterion for
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::23863aed34edbe6518c60ac4d0e8c79e
Publikováno v:
Journal of Fixed Point Theory and Applications. 21
Based on the theory of ball spaces introduced by Kuhlmann and Kuhlmann, we introduce and study Caristi–Kirk and Oettli–Théra ball spaces. We show that if the underlying metric space is complete, then these have a very strong property: every ball
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::60dc8c52e605a084f9efd966deed3492
https://doi.org/10.1007/s11784-019-0729-4
https://doi.org/10.1007/s11784-019-0729-4
Autor:
Alessandro Linzi
Publikováno v:
Web of Science
The main aim of this article is to study and develop valuation theory for Krasner hyperfields. In analogy with classical valuation theory for fields, we generalise the formalism of valuation rings to describe equivalence of valuations on hyperfields.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5730b29f8ecde69fb64edfeb729ec1bb
https://publons.com/wos-op/publon/56316591/
https://publons.com/wos-op/publon/56316591/
