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2. Polygroup objects in regular categoriesAlessandro Linzi, 2024, original scientific article Abstract: 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: 1361; Downloads: 6
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4. Regular local hyperrings and hyperdomainsHashem Bordbar, Irina Elena Cristea, Sanja Rasovic, 2022, original scientific article Abstract: This paper falls in the area of hypercompositional algebra. In particular, it focuses on the
class of Krasner hyperrings and it studies the regular local hyperrings. These are Krasner hyperrings R with a unique maximal hyperideal M having the dimension equal to the dimension of the vectorial hyperspace M. The aim of the paper is to show that any regular local hyperring is a hyperdomain. M2 For proving this, we make use of the relationship existing between the dimension of the vectorial hyperspaces related to the hyperring R and to the quotient hyperring R = R , where a is an element in M \ M2, and of the regularity of R.
Keywords: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Published in RUNG: 27.09.2022; Views: 1636; Downloads: 27
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10. Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures2020, scientific monograph Keywords: symmetry, hypergroup, hyperring, hyperfield, fundamental relation, rough set, fuzzy set, multiset, soft set, hyperhomography, BCK-algebra, multiautomatom, artificial neuron, hypergraph
Published in RUNG: 27.03.2020; Views: 3248; Downloads: 0
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