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1.
Polygroup objects in regular categories
Alessandro 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: 393; Downloads: 3
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2.
ON HYPERIDEALS OF KRASNER HYPERRINGS BASED ON DERIVED UNITARY RINGS
Seyed Mousavi, Morteza Jafarpour, Hojat Babaei, Irina Elena Cristea, 2022, original scientific article

Keywords: (Krasner) hyperring, strongly regular relation, λe-closed hy- perideal.
Published in RUNG: 11.05.2022; Views: 1799; Downloads: 0
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3.
4.
A note on the support of a hypermodule
Hashem Bordbar, Michal Novak, Irina Elena Cristea, 2020, original scientific article

Keywords: Krasner hyperring, prime/maximal hyperideal, length of hypermodules, annihilator of hypermodules, support of hypermodules
Published in RUNG: 28.02.2019; Views: 3411; Downloads: 0
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5.
Overview on the height of a hyperideal in Krasner hyperrings
Hashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, published scientific conference contribution abstract

Keywords: Krasner hyperring, prime hyperideal, Noetherian hyperring
Published in RUNG: 30.08.2017; Views: 3860; Downloads: 0
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6.
HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS
Hashem Bordbar, Irina Elena Cristea, Michal Novak, 2017, original scientific article

Abstract: Inspired by the classical concept of height of a prime ideal in a ring, we proposed in a precedent paper the notion of height of a prime hyperideal in a Krasner hyperring. In this note we first generalize some results concerning the height of a prime hyperideal in a Noetherian Krasner hyperring, with the intent to extend this definition to the case of a general hyperideal in a such hyperring. The main results in this note show that, in a commutative Noetherian Krasner hyperring, the height of a minimal prime hyperideal over a proper hyperideal generated by n elements is less than or equal to n, the converse of this claim being also true. Based on this result, it can be proved that the height of such a prime hyperideal is limited by the height of a corresponding quotient hyperideal.
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published in RUNG: 01.06.2017; Views: 4654; Downloads: 0
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