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1.
The Structure of the Block Code Generated by a BL-Algebra
Hashem Bordbar, 2022, original scientific article

Abstract: Inspired by the concept of BL-algebra as an important part of the ordered algebra, in this paper we investigate the binary block code generated by an arbitrary BL-algebra and study related properties. For this goal, we initiate the study of the BL-function on a nonempty set P based on BL-algebra L, and by using that, l-functions and l-subsets are introduced for the arbitrary element l of a BL-algebra. In addition, by the mean of the l-functions and l-subsets, an equivalence relation on the BL-algebra L is introduced, and using that, the structure of the code generated by an arbitrary BL-algebra is considered. Some related properties (such as the length and the linearity) of the generated code and examples are provided. Moreover, as the main result, we define a new order on the generated code C based on the BL-algebra L, and show that the structures of the BL-algebra with its order and the correspondence generated code with the defined order are the same.
Found in: osebi
Keywords: BL-function, BL-code, binary linear block codes, coding theory, BL-algebra
Published: 07.03.2022; Views: 534; Downloads: 20
.pdf Fulltext (261,87 KB)

2.
HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGS
Hashem Bordbar, Irina 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.
Found in: osebi
Keywords: Krasner hyperring, prime/maximalhyperideal, Noetherian hyperring, height of a prime hyperideal
Published: 01.06.2017; Views: 3478; Downloads: 0
.pdf Fulltext (138,31 KB)

3.
Overview on the height of a hyperideal in Krasner hyperrings
Hashem Bordbar, Irina Cristea, Michal Novak, 2017, published scientific conference contribution abstract

Found in: osebi
Keywords: Krasner hyperring, prime hyperideal, Noetherian hyperring
Published: 30.08.2017; Views: 2794; Downloads: 0
.pdf Fulltext (1,59 MB)

4.
Neutrosophic N-Structures Applied to BCK/BCI-Algebras
Jun young Bae, Florentin Smarandache, Hashem Bordbar, 2017, original scientific article

Abstract: Neutrosophic N-structures with applications in BCK/BCI-algebras is discussed. The notions of a neutrosophic N-subalgebra and a (closed) neutrosophic N-ideal in a BCK/BCI-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N-subalgebra and a neutrosophic N-ideal are considered, and relations between a neutrosophic N-subalgebra and a neutrosophic N-ideal are stated. Conditions for a neutrosophic N-ideal to be a closed neutrosophic N-ideal are provided.
Found in: osebi
Keywords: neutrosophic N-structure, neutrosophic N-subalgebra, (closed) neutrosophic N-ideal
Published: 01.12.2019; Views: 1919; Downloads: 0
.pdf Fulltext (261,83 KB)

5.
Italian journal of pure and applied mathematics
2010, other performed works

Abstract: Član uredniškega odbora 2020-
Found in: osebi
Published: 15.04.2021; Views: 1044; Downloads: 97
URL Fulltext (0,00 KB)
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6.
Neutrosophic sets and systems
other performed works

Abstract: urednik 2020-
Found in: osebi
Published: 15.04.2021; Views: 1016; Downloads: 79
URL Fulltext (0,00 KB)
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7.
Symmetry
2009, other performed works

Abstract: recenzent 2021-
Found in: osebi
Keywords: physics, chemistry, biology, mathematics, computer science, engineering
Published: 15.04.2021; Views: 1094; Downloads: 45
.docx Fulltext (266,05 KB)
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8.
Supplements Related to Normal p-Projective Hypermodules
Burcu Turkmen, Hashem Bordbar, Irina Cristea, 2022, original scientific article

Abstract: In this study, the role of supplements in Krasner hypermodules is examined and related to normal p-projectivity. We prove that the class of supplemented Krasner hypermodules is closed under finite sums and under quotients. Moreover, we give characterizations of finitely generated supplemented and amply supplemented Krasner hypermodules. In the second part of the paper we relate the normal projectivity to direct summands and supplements in Krasner hypermodules.
Found in: osebi
Keywords: direct summand, normal p-projective hypermodule, supplement subhypermodule, small subhypermodule
Published: 06.06.2022; Views: 349; Downloads: 0
.pdf Fulltext (309,59 KB)

9.
Regular local hyperrings and hyperdomains
Hashem Bordbar, Irina 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.
Found in: osebi
Keywords: hyperring, hypermodule, vectorialhyperspace, dimension, regularhyperring, regular parameter element, hyperdomain
Published: 27.09.2022; Views: 165; Downloads: 6
.pdf Fulltext (258,07 KB)

10.
Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social Systems
Narjes Firouzkouhi, Reza Ameri, Abbas Amini, Hashem Bordbar, 2022, original scientific article

Abstract: Graph theoretic techniques have been widely applied to model many types of links in social systems. Also, algebraic hypercompositional structure theory has demonstrated its systematic application in some problems. Influenced by these mathematical notions, a novel semihypergroup based graph (SBG) of G = hH, Ei is constructed through the fundamental relation gn on H, where semihypergroup H is appointed as the set of vertices and E is addressed as the set of edges on SBG. Indeed, two arbitrary vertices x and y are adjacent if xgny. The connectivity of graph G is characterized by xg y, whereby the connected components SBG of G would be exactly the elements of the fundamental group H/g . Based on SBG, some fundamental characteristics of the graph such as complete, regular, Eulerian, isomorphism, and Cartesian products are discussed along with illustrative examples to clarify the relevance between semihypergroup H and its corresponding graph. Furthermore, the notions of geometric space, block, polygonal, and connected components are introduced in terms of the developed SBG. To formulate the links among individuals/countries in the wake of the COVID (coronavirus disease) pandemic, a theoretical SBG methodology is presented to analyze and simplify such social systems. Finally, the developed SBG is used to model the trend diffusion of the viral disease COVID-n in social systems (i.e., countries and individuals).
Found in: osebi
Keywords: graph theory, hypergroup, fundamental relation, social systems, geometric space
Published: 23.11.2022; Views: 69; Downloads: 0
.pdf Fulltext (4,16 MB)

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