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1.
Polygroup objects in regular categories
Alessandro Linzi, 2024, izvirni znanstveni članek

Opis:

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 structure induced on the category $ {\mathbf{Rel}} $ of sets and relations by cartesian products. We highlight how our approach can be generalised to any regular category. In addition, we consider the theory of partial multirings and find fully faithful functors between certain slice or coslice categories of the category of partial multirings and other categories formed by well-known mathematical structures and their morphisms.


Ključne besede: polygroup, canonical hypergroup, multiring, Krasner hyperring, regular category, relation
Objavljeno v RUNG: 25.03.2024; Ogledov: 392; Prenosov: 3
.pdf Celotno besedilo (504,37 KB)
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2.
A result of Krasner in categorial form
Alessandro Linzi, 2023, izvirni znanstveni članek

Ključne besede: valuation, completion, field, hyperfield, category theory
Objavljeno v RUNG: 11.12.2023; Ogledov: 782; Prenosov: 6
.pdf Celotno besedilo (347,74 KB)
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3.
On the deep connection between hyperstructures and quantum logic
Nicolò Cangiotti, Alessandro Linzi, 2023, objavljeni povzetek znanstvenega prispevka na konferenci

Opis: We describe and motivate our project for a hypercompositional approach to quantum logic.
Ključne besede: quantum logic, hypercompositional algebra, hypergroups, lattice, projective geometry
Objavljeno v RUNG: 01.08.2023; Ogledov: 862; Prenosov: 3
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A new symmetry in valuation theory
Alessandro Linzi, 2023, objavljeni povzetek znanstvenega prispevka na konferenci

Ključne besede: valuation, valued field, p-adic numbers, hyperfield
Objavljeno v RUNG: 27.06.2023; Ogledov: 1070; Prenosov: 8
.pdf Celotno besedilo (405,62 KB)

6.
Valuations on structures more general than fields
Alessandro Linzi, 2023, objavljeni znanstveni prispevek na konferenci

Ključne besede: hyperfield, valuation, valued field, tropical hyperfield
Objavljeno v RUNG: 27.06.2023; Ogledov: 955; Prenosov: 9
.pdf Celotno besedilo (276,86 KB)
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7.
On an algebraic description of projective geometries
Alessandro Linzi, predavanje na tuji univerzi

Ključne besede: Projective geometry, projective space, hypergroup
Objavljeno v RUNG: 06.06.2023; Ogledov: 1256; Prenosov: 0
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8.
Characteristic, C-characteristic and positive cones in hyperfields
Dawid Edmund Kędzierski, Alessandro Linzi, Hanna Stojałowska, 2023, izvirni znanstveni članek

Opis: We study the notions of positive cone, characteristic and C-characteristic in (Krasner) hyperfields. We show how these interact in order to produce interesting results in the theory of hyperfields. For instance, we give a criterion for deciding whether certain hyperfields cannot be obtained via Krasner's quotient construction. We prove that any positive integer (larger than 1) can be realized as the characteristic of some infinite hyperfield and an analogous result for C-characteristic. Finally, we study the (directed) graph associated to the strict partial order induced by a positive cone in a hyperfield in various examples.
Ključne besede: hyperfield, order, characteristic, positive cone
Objavljeno v RUNG: 13.02.2023; Ogledov: 1108; Prenosov: 3
.pdf Celotno besedilo (372,22 KB)
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9.
Dependence relations and grade fuzzy set
Alessandro Linzi, Irina Elena Cristea, 2023, izvirni znanstveni članek

Opis: 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 degree of influence. Its definition is based on a partial hyperoperation and a directed graph which we associate with any dependence relation. We compute the degree of influence in various examples and prove some general properties. Among these properties, we find symmetries that have the potential to be applied in the realization of effective algorithms for the computations.
Ključne besede: dependence relation, degree of influence, grade fuzzy set, hypercompositional structure, hyperoperation
Objavljeno v RUNG: 23.01.2023; Ogledov: 1479; Prenosov: 3
.pdf Celotno besedilo (304,05 KB)
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10.
Algebraic hyperstructures in the model theory of valued fields : PhD in mathematics
Alessandro Linzi, 2022, doktorska disertacija

Ključne besede: hyperfield, valued field, algebra, model theory, quantifier elimination
Objavljeno v RUNG: 27.10.2022; Ogledov: 1478; Prenosov: 82
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