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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: 759; Downloads: 4
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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: 1159; Downloads: 11
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On the deep connection between hyperstructures and quantum logic
Nicolò Cangiotti, Alessandro Linzi, 2023, published scientific conference contribution abstract

Abstract: We describe and motivate our project for a hypercompositional approach to quantum logic.
Keywords: quantum logic, hypercompositional algebra, hypergroups, lattice, projective geometry
Published in RUNG: 01.08.2023; Views: 1045; Downloads: 3
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Determining the Optimal Flows in Zero-Time Dynamic Networks
Ahmad Hosseini, Fardin Dashty Saridarq, 2012, original scientific article

Keywords: Linear algebra, Networks/graphs, Linear programming
Published in RUNG: 15.02.2023; Views: 1392; Downloads: 1
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Algebraic hyperstructures in the model theory of valued fields : PhD in mathematics
Alessandro Linzi, 2022, doctoral dissertation

Keywords: hyperfield, valued field, algebra, model theory, quantifier elimination
Published in RUNG: 27.10.2022; Views: 1708; Downloads: 90
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Special Issue on Symmetry in Classical and Fuzzy Algebraic Hypercompositional Structures
Irina Elena Cristea, 2022, other scientific articles

Keywords: symmetry, hypercompositional algebra, special issue
Published in RUNG: 17.10.2022; Views: 1302; Downloads: 20
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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.
Keywords: BL-function, BL-code, binary linear block codes, coding theory, BL-algebra
Published in RUNG: 07.03.2022; Views: 1742; Downloads: 50
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Codes generated by ordered algebraic structures
Hashem Bordbar, 2021, published scientific conference contribution abstract

Abstract: Error-control codes are used to detect and correct errors that occur when data are trans-mitted across some noisy channel or stored on some medium. The study of error-control codes is called coding theory and emerged in 1948 by Claud Shannon's paper which demonstrated that by proper encoding of the data, errors induced by a noisy channel can be reduced to any desired level without sacrificing the rate of information transmission. Some algebraic structures, includes the study and discovery of various coding schemes, are used to increase the number of errors that can be corrected during data transmission. One of the classes of logical algebra is ordered algebras which were introduced by Imai and Iseki in 1966. In this note, I study the codes generating by the ordered algebraic structures such as BCK-algebras and BL-algebras. For this goal, symmetric rela-tions on these ordered structures facilitate us to design the correspondence codeword. Moreover, I show that the structure of ordered algebra and the code generated by it will be the same.
Keywords: coding theory, BCK-algebra, BL-algebra
Published in RUNG: 20.08.2021; Views: 2219; Downloads: 151
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