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1.
Łukasiewicz anti fuzzy subalgebras of BCK/BCI-algebras
Jeong Gi Kang, Hashem Bordbar, 2025, original scientific article

Abstract: The subalgebra of BCK/BCI-algebra using Łukasiewicz anti fuzzy set introduced by Jun is studied in this article. The concept of Łukasiewicz anti fuzzy subalgebra of a BCK/BCI-algebra is introduced, and several properties are investigated. The relationship between anti fuzzy subalgebra and Łukasiewicz anti fuzzy subalgebra is given, and characterization of a Łukasiewicz anti fuzzy subalgebra is discussed. Conditions are found in which a Lukasiewicz anti fuzzy set is a Lukasiewicz anti fuzzy subalgebra Finally, conditions under which ⋖-subset, Υsubset, and anti-subset become subalgebra are explored.
Keywords: anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy, subalgebra, Υ-subset, anti subset
Published in RUNG: 30.10.2024; Views: 232; Downloads: 0
.pdf Full text (406,85 KB)

2.
A characterization of normal injective and normal projective hypermodules
Ergül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article

Abstract: This study is motivated by the recently published papers on normal injective and normal projective hypermodules. We provide a new characterization of the normal injective and normal projective hypermodules by using the splitting of the short exact sequences of hypermodules. After presenting some of their fundamental properties, we show that if a hypermodule is normal projective, then every exact sequence ending with it is splitting. Moreover, if a hypermodule is a normal injective, then every exact sequence starting with it is splitting as well. Finally, we investigate the relationships between semisimple, simple, normal injective, and normal projective hypermodules.
Keywords: short exact sequence, normal injective hypermodule, normal projective hypermodule
Published in RUNG: 20.06.2024; Views: 735; Downloads: 6
.pdf Full text (277,55 KB)
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3.
Categorical approach of normal injective and torsionable hypermodules
Hashem Bordbar, 2024, published scientific conference contribution abstract

Abstract: Inspired by the characterization of injective objects in category theory, our main purpose in this research is to investigate the relationships of di- visible and injective hypermodules with torsion elements and torsionable hypermodules with a category approach. These days, it is extremely tempt- ing to do the research in an Abelian category, so we discuss these topics in an Abelian category. For a Krasner R-hypermodule M, we ex- tend the definition of a zero-divisor element of R to a zero-divisor ele- ment of R over M, and then the definition of divisible R-hypermodule is introduced. Be- sides, the torsion element and torsionable hypermodule are introduced and we show that every torsionable R-hypermodule M is a normal injective, where R is a commutative hyperring.
Keywords: hypermodules, hyperrings, normal injective, normal projective
Published in RUNG: 18.06.2024; Views: 777; Downloads: 0
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4.
A hyperstructural approach to semisimplicity
Ergül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, original scientific article

Abstract: In this paper, we provide the basic properties of (semi)simple hypermodules. We show that if a hypermodule M is simple, then (End(M), ·) is a group, where End(M) is the set of all normal endomorphisms of M. We prove that every simple hypermodule is normal projective with a zero singular subhypermodule. We also show that the class of semisimple hypermodules is closed under internal direct sums, factor hypermodules, and subhypermodules. In particular, we give a characterization of internal direct sums of subhypermodules of a hypermodule.
Keywords: direct sum, simple hypermodule, semisimple hypermodule
Published in RUNG: 31.01.2024; Views: 1406; Downloads: 14
.pdf Full text (328,98 KB)
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5.
Sheffer stroke Hilbert algebras stabilizing by ideals
Tugce Katican, Hashem Bordbar, 2024, original scientific article

Abstract: This manuscript aims to provide a new characterization of Sheffer stroke Hilbert algebras due to their ideals and proposes stabilizers. In the setup of the main results, we construct particular subsets of Sheffer stroke Hilbert algebras and we propose important properties of these subsets by investigating whether these sets are ideals or not. Furthermore, we investigate whether the introduced subsets of Sheffer stroke Hilbert algebras are minimal ideals. Afterward, we define stabilizers in a Sheffer stroke Hilbert algebra and obtain their set theoretical properties. As an implementation of the theoretical findings, we present numerous examples and illustrative remarks to guide readers.
Keywords: Hilbert algebra, Sheffer operation, ideal, stabilizer
Published in RUNG: 31.01.2024; Views: 1245; Downloads: 8
.pdf Full text (320,63 KB)
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6.
Torsion elements and torsionable hypermodules
Hashem Bordbar, 2023, original scientific article

Abstract: This article is motivated by the recently published studies on divisible hypermodules and falls in the area of hypercompositional algebra. In particular, it focuses on the torsion elements in Krasner hypermodules. First, we define the concept of a torsion element over a hypermodule, and based on it, we introduce a new class of hypermodules, namely the torsionable hypermodule. After investigating some of their fundamental properties, we will show that the class of torsionable hypermodules is a subclass of the class of divisible hypermodules. Finally, we present the relationships between divisible, torsionable, and normal injective hypermodules.
Keywords: hypermodules, zero divisors, torsion elements, torsionable hypermodules, normal injective hypermodules
Published in RUNG: 03.11.2023; Views: 1528; Downloads: 4
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7.
Algebraic structures and graph theory
scientific monograph

Keywords: graphs, Cayley graph, graph energy, hypergraphs, semigroups, algebra, hypergroups, hyperfield
Published in RUNG: 10.08.2023; Views: 1661; Downloads: 12
.pdf Full text (4,26 MB)
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8.
Preface to the special issue ʺAlgebraic structures and graph theoryʺ : editorial
Irina Elena Cristea, Hashem Bordbar, 2023, other scientific articles

Keywords: algebraic structure, graphs
Published in RUNG: 27.07.2023; Views: 1490; Downloads: 9
.pdf Full text (205,60 KB)
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9.
10.
ŁUKASIEWICZ ANTI FUZZY SUBALGEBRAS OF BCK/BCI-ALGEBRAS
Jeong Gi Kang, Hashem Bordbar, 2025, original scientific article

Abstract: Abstract. The subalgebra of BCK/BCI-algebra using Łukasiewicz anti fuzzy set introduced by Jun is studied in this article. The concept of Łukasiewicz anti fuzzy subalgebra of a BCK/BCI-algebra is introduced, and several properties are investigated. The relationship between anti fuzzy subalgebra and Łukasiewicz anti fuzzy subalgebra is given, and the characterization of a Łukasiewicz anti fuzzy subalgebra is discussed. Conditions are found in which a Lukasiewicz anti fuzzy set is a Lukasiewicz anti fuzzy subalgebra Finally, conditions under which ⋖-subset, Υ- subset, and anti-subset become subalgebra are explored.
Keywords: Anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy subalgebra, ⋖-subset, Υ-subset, anti subset
Published in RUNG: 20.02.2023; Views: 1651; Downloads: 0
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