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Polygroup objects in regular categories
Alessandro Linzi, 2024, original scientific article


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.

Keywords: polygroup, canonical hypergroup, multiring, Krasner hyperring, regular category, relation
Published in RUNG: 25.03.2024; Views: 479; Downloads: 3
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New aspects in the theory of complete hypergroups
Irina Elena Cristea, 2023, published scientific conference contribution

Keywords: complete hypergroup, reversibility, period of an element regularity, reducibility, class equation, commutativity degree, Euler's totient function
Published in RUNG: 20.06.2023; Views: 1217; Downloads: 8
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On an algebraic description of projective geometries
Alessandro Linzi, invited lecture at foreign university

Keywords: Projective geometry, projective space, hypergroup
Published in RUNG: 06.06.2023; Views: 1357; Downloads: 0
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New aspects in the theory of complete hypergroups
Irina Elena Cristea, published scientific conference contribution abstract

Keywords: hypergroup, complete part, reversibility, reducibility, class equation, commutativity degree
Published in RUNG: 08.03.2023; Views: 1159; Downloads: 14
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Eulerʹs totient function applied to complete hypergroups
Andromeda Cristina Sonea, Irina Elena Cristea, 2023, original scientific article

Keywords: Euler's totient function, complete hypergroups, period of an element, heart of a hypergroup
Published in RUNG: 19.01.2023; Views: 1480; Downloads: 3
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Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social Systems
Narjes Firouzkouhi, Reza Ameri, Abbas Amini, Hashem Bordbar, 2022, original scientific article

Abstract: Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup based graph (SBG) of G = hH, Ei is constructed through the fundamental relation gn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xgny. The connectivity of graph G is characterized by xg y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/g . Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).
Keywords: graph theory, hypergroup, fundamental relation, social systems, geometric space
Published in RUNG: 23.11.2022; Views: 1173; Downloads: 0
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Divisible hypermodules
Hashem Bordbar, Irina Elena Cristea, 2022, original scientific article

Keywords: normal injective hypermodule, zero divisor, divisible hypermodule, canonical hypergroup
Published in RUNG: 11.02.2022; Views: 1971; Downloads: 34
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