TENSORIAL ALGEBRA

D. I. Dzeboev

About the authors

D. I. Dzeboev

Дзебоев Д. И. – стажёр-исследователь, НИУ ВШЭ, Факультет компьютерных наук, Лаборатория моделирования и управления сложными системами, 109028, Москва, Покровский бульвар, 11. Область научных интересов: Тензориальная алгебра, гиперкомплексные числа, неассоциативные структуры, искусственный интеллект, нейронные сети. Orcid 0009-0008-4004-8750

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UDC: 512.554.1
DOI: 10.24412/2413-7383-2025-3-38-11-18
Language: Russian

Abstract: The aim of this study is to develop and substantiate a new universal method for defining multiplication, applicable to a wide class of algebraic systems. The proposed solution is based on the introduction of Tensorial Algebra, where the product is determined through a third -order algebra tensor. This approach makes it possible to specify or to learn multiplication rules in arbitrary algebras and ensures the preservation of dimensionality in operations. It is shown that the proposed method generalizes hypercomplex systems and opens up prospec ts for applications in the theory of non - associative algebras, as well as in problems of mathematical modeling and computational algebra.

Keywords: tensorial algebra, hypercomplex numbers, non-associative algebras, multiplication structures, algebraic systems

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Issue: 3(38)'2025
Section: ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING
How to cite: D. I. Dzeboev. TENSORIAL ALGEBRA // Problems of Artificial Intelligence. - 2025. - № 3 (38). - P. 11-18. - https://paijournal.guiaidn.ru/en/2025/3(38)-2.html

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