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1.
Hyperideal-based zero-divisor graph of the general hyperring Z[sub]n
Mohammad Hamidi, Irina Elena Cristea, 2024, original scientific article

Keywords: general hyperring, hyperideal, absorbing element, hyperideal-based zero-divisor graph
Published in RUNG: 08.05.2024; Views: 524; Downloads: 3
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2.
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: 669; Downloads: 3
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3.
Orderings and valuations in hyperfields
Katarzyna Kuhlmann, Alessandro Linzi, Hanna Stojałowska, 2022, original scientific article

Keywords: hyperfields, hyperring, ordering, valuation
Published in RUNG: 28.09.2022; Views: 1414; Downloads: 0
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4.
Regular local hyperrings and hyperdomains
Hashem 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: 1346; Downloads: 24
.pdf Full text (258,07 KB)

5.
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: 2003; Downloads: 0
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6.
The Reducibility Concept in General Hyperrings
Irina Elena Cristea, Milica Kankaraš, 2021, original scientific article

Keywords: general hyperring, reducibility, fundamental relation, equivalence
Published in RUNG: 25.08.2021; Views: 2019; Downloads: 45
.pdf Full text (302,45 KB)

7.
8.
Some open problems in hypercompositional algebra
Irina Elena Cristea, 2020, published scientific conference contribution abstract (invited lecture)

Keywords: hypergroup, hyperring, hyperfield, hypermodule, dependence relation, fundamental realtion, fuzzy reducibility
Published in RUNG: 23.06.2020; Views: 3165; Downloads: 0
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9.
A Comparison of Complete Parts on m-Idempotent Hyperrings
Azam Adineh Zadeh, Morteza Norouzi, Irina Elena Cristea, 2020, original scientific article

Keywords: hyperring, m-idempotent hyperring, ξm-parts, ξm-complete hyperrings
Published in RUNG: 06.04.2020; Views: 2858; Downloads: 85
.pdf Full text (286,29 KB)

10.
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