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


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: 199; Prenosov: 3
.pdf Celotno besedilo (504,37 KB)
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From HX-groups to HX-polygroups
Seyed S. Mousavi, Morteza Jafarpour, Irina Elena Cristea, 2023, izvirni znanstveni članek

Ključne besede: HX-group, hypercompositional structure, coset, polygroup, regularity, uniformity, essentiality, double coset
Objavljeno v RUNG: 22.12.2023; Ogledov: 556; Prenosov: 7
.pdf Celotno besedilo (340,31 KB)
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On Factorizable Semihypergroups
Dariush Heidari, Irina Elena Cristea, 2020, izvirni znanstveni članek

Ključne besede: semihypergroup, factorization, regular semihypergroup, polygroup
Objavljeno v RUNG: 01.07.2020; Ogledov: 2251; Prenosov: 77
.pdf Celotno besedilo (229,27 KB)

Heidari, D.[Heidari, Dariush](IR-MIHES);Davvaz, B.[Davvaz, Bijan](IR-YAZD-M)Characterization of small polygroups by their fundamental groups.
2020, recenzija, prikaz knjige, kritika

Ključne besede: Maple, polygroup, isomorphism, fundamental group
Objavljeno v RUNG: 06.04.2020; Ogledov: 2411; Prenosov: 0
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Subpolygroups related to a fuzzy topology
N. Abbasizadeh, Irina Elena Cristea, Bijan Davvaz, Jianming Zhan, 2018, izvirni znanstveni članek

Ključne besede: polygroup, fuzzy topological space, (relatively) fuzzy continuity, lower (upper) fuzzy topological subpolygroup
Objavljeno v RUNG: 21.08.2018; Ogledov: 3325; Prenosov: 0
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Left almost polygroups
Naveed Yaqoob, Irina Elena Cristea, Muhhamad Gulistan, Shah Nawaz, 2018, izvirni znanstveni članek

Opis: In this introductory note we define the concept of left almost polygroup and provide several examples. We also discuss the quotient structure and isomorphism theorems for left almost polygroups.
Ključne besede: left almost polygroup, direct product, hyperorder, homomorphism
Objavljeno v RUNG: 28.03.2018; Ogledov: 3669; Prenosov: 0
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