1. Matematika za gospodarski inženiringIrina Elena Cristea, Hashem Bordbar, Alessandro Linzi, 2024, univerzitetni, visokošolski ali višješolski učbenik z recenzijo Ključne besede: linearna algebra, funkcije, limite, zveznost, diferencialni račun, integrabilnost, funkcije več spremenljivk, diferencialne enačbe
Objavljeno v RUNG: 09.12.2024; Ogledov: 125; Prenosov: 0
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2. Ordered algebraic structure in a linear codeHashem Bordbar, 2024, izvirni znanstveni članek Opis: In this article, we initiate an exploration of the algebraic structures
within coding theory. Specifically, we focus on the potential for an ordered al-
gebraic structure, known as a BCI-algebra, within an arbitrary linear code
C. We demonstrate that any binary linear code C of length n, where n is
a positive integer, can be equipped with a BCI-algebra structure between its
codewords. This structure is called BCI-algebra over the code C and denoted
by (BCI)C -algebra. To establish this structure, we define an operation ∗C be-
tween the codewords and investigate its properties. Additionally, we introduce
the concept of subcodes within a code and examine the relationship between
these subcodes and the ideals of a BCI-algebra over code C. Furthermore,
we define a binary relation among codewords and prove that code C, under
this relation—referred to as the (BCI)C -order—forms a partially ordered set.
Lastly, we show that the generator matrix of a binary linear code C contains
the minimal codewords of C with respect to the (BCI)C -order.
Ključne besede: BCI-algebra, binary linear block codes, subcodes, partially ordered set, lexicographic order
Objavljeno v RUNG: 05.12.2024; Ogledov: 200; Prenosov: 2
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4. Łukasiewicz anti fuzzy subalgebras of BCK/BCI-algebrasJeong Gi Kang, Hashem Bordbar, 2025, izvirni znanstveni članek Opis: 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.
Ključne besede: anti fuzzy subalgebra, Łukasiewicz anti fuzzy set, Łukasiewicz anti fuzzy, subalgebra, Υ-subset, anti subset
Objavljeno v RUNG: 30.10.2024; Ogledov: 404; Prenosov: 0
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5. A characterization of normal injective and normal projective hypermodulesErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, izvirni znanstveni članek Opis: 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.
Ključne besede: short exact sequence, normal injective hypermodule, normal projective hypermodule
Objavljeno v RUNG: 20.06.2024; Ogledov: 840; Prenosov: 6
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6. Categorical approach of normal injective and torsionable hypermodulesHashem Bordbar, 2024, objavljeni povzetek znanstvenega prispevka na konferenci Opis: 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.
Ključne besede: hypermodules, hyperrings, normal injective, normal projective
Objavljeno v RUNG: 18.06.2024; Ogledov: 875; Prenosov: 0
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7. A hyperstructural approach to semisimplicityErgül Türkmen, Burcu Nİşancl Türkmen, Hashem Bordbar, 2024, izvirni znanstveni članek Opis: 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.
Ključne besede: direct sum, simple hypermodule, semisimple hypermodule
Objavljeno v RUNG: 31.01.2024; Ogledov: 1576; Prenosov: 14
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8. Sheffer stroke Hilbert algebras stabilizing by idealsTugce Katican, Hashem Bordbar, 2024, izvirni znanstveni članek Opis: 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.
Ključne besede: Hilbert algebra, Sheffer operation, ideal, stabilizer
Objavljeno v RUNG: 31.01.2024; Ogledov: 1361; Prenosov: 8
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9. Torsion elements and torsionable hypermodulesHashem Bordbar, 2023, izvirni znanstveni članek Opis: 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.
Ključne besede: hypermodules, zero divisors, torsion elements, torsionable hypermodules, normal injective hypermodules
Objavljeno v RUNG: 03.11.2023; Ogledov: 1654; Prenosov: 4
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