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: 304; Downloads: 9
 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: 3208; 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: 135; Downloads: 0
Fulltext (309,59 KB) |
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