1. The Structure of the Block Code Generated by a BL-AlgebraHashem 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 Fulltext (261,87 KB) |
2. HEIGHT OF HYPERIDEALS IN NOETHERIAN KRASNER HYPERRINGSHashem 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 Fulltext (138,31 KB) |
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8. Supplements Related to Normal p-Projective HypermodulesBurcu 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 Fulltext (309,59 KB) |
9. Regular local hyperrings and hyperdomainsHashem 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 Fulltext (258,07 KB) |
10. Semihypergroup-Based Graph for Modeling International Spread of COVID-n in Social SystemsNarjes 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 Fulltext (4,16 MB) |