2 citations · 3 across the 10 of their papers we have counts for
11 papers
Valued Mosaics
Alessandro Linzi
Nakamura--Reyes showed that the category of commutative mosaics---unital reversible hypermagmas, without associativity---is complete, cocomplete, and has free objects, in contrast…
Finite-field Krasner quotients: isomorphism thresholds, characteristics, and censuses
Alessandro Linzi
We study Krasner quotient hyperfields arising from finite fields, , where has index . Building on the structure theorem of Baker--Jin, we determine…
L-Mosaics and Bounded Join-Semilattices in Isabelle/HOL
Alessandro Linzi
We present a complete formalization in Isabelle/HOL of the object part of an equivalence between L-mosaics and bounded join-semilattices, employing an AI-assisted methodology that…
L-mosaics and orthomodular lattices
Nicolò Cangiotti, Alessandro Linzi, Enrico Talotti
In this paper, we introduce a class of hypercompositional structures called dualizable L-mosaics. We prove that their category is equivalent to that formed by ortholattices and we…
A result of Krasner in categorial form
Alessandro Linzi
In 1957 M.\ Krasner described a complete valued field via the projective limit of a system of certain structures, called hyperfields, associated to . We put this res…
On projective spaces over local fields
Nicolò Cangiotti, Alessandro Linzi
Let be the set of points of a finite-dimensional projective space over a local field , endowed with the topology naturally induced from the canonical topology…
Notes on valuation theory for Krasner hyperfields
Alessandro Linzi
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…
On the hyperfields associated to valued fields
Alessandro Linzi, Pierre Touchard
One can associate to a valued field an inverse system of valued hyperfields in a natural way. We investigate when, conversely, such a system arise from…
Orderings and valuations in hyperfields
Katarzyna Kuhlmann, Alessandro Linzi, Hanna Stojałowska
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 induc…
Hypervaluations on hyperfields and ordered canonical hypergroups
Alessandro Linzi, Hanna Stojałowska
We study the concept of hypervaluations on hyperfields. In particular, we show that any hypervaluation from a hyperfield onto an ordered canonical hypergroup is the composition of…
Caristi-Kirk and Oettli-Théra Ball Spaces and applications
Piotr Błaszkiewicz, Hanna Ćmiel, Alessandro Linzi +1
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…