拟约当代数的同伦

IF 1.9 3区数学 Q1 MATHEMATICS, APPLIED Axioms Pub Date : 2023-11-10 DOI:10.3390/axioms12111045

Reem K. Alhefthi, Akhlaq A. Siddiqui, Fatmah B. Jamjoom

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引用次数: 0

摘要

准约当代数的概念最初是由委拉斯开兹和费利佩提出的。后来，M. R. Bremner提供了一个叫做K-B准约当代数的修改;它们包括所有的约当代数和所有的对偶代数，因此也包括所有的结合代数。任何拟约当代数都是特殊的，如果它与某些对偶代数的拟约当子代数同构。考虑到同伦在约当代数理论中的关键作用，我们开始研究拟约当代数的同伦;在其他相关结果中，我们证明了任何特殊拟约当代数的同伦是特殊拟约当代数，K-B拟约当代数的同伦是拟约当代数。在续文中，我们也给出了一些开放的问题。

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Homotopes of Quasi-Jordan Algebras

The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative algebras. Any quasi-Jordan algebra is special if it is isomorphic to a quasi-Jordan subalgebra of some dialgebras. Keeping in view the pivotal role of homotopes in the theory of Jordan algebras, we begin a study of the homotopes of quasi-Jordan algebras; among other related results, we show that the homotopes of any special quasi-Jordan algebra are special quasi-Jordan algebras and that the homotopes of a K-B quasi-Jordan algebra is a quasi-Jordan algebra. In the sequel, we also give some open problems.

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来源期刊

Axioms Mathematics-Algebra and Number Theory

自引率

10.00%

发文量

604

审稿时长

11 weeks

期刊介绍： Axiomatic theories in physics and in mathematics (for example, axiomatic theory of thermodynamics, and also either the axiomatic classical set theory or the axiomatic fuzzy set theory) Axiomatization, axiomatic methods, theorems, mathematical proofs Algebraic structures, field theory, group theory, topology, vector spaces Mathematical analysis Mathematical physics Mathematical logic, and non-classical logics, such as fuzzy logic, modal logic, non-monotonic logic. etc. Classical and fuzzy set theories Number theory Systems theory Classical measures, fuzzy measures, representation theory, and probability theory Graph theory Information theory Entropy Symmetry Differential equations and dynamical systems Relativity and quantum theories Mathematical chemistry Automata theory Mathematical problems of artificial intelligence Complex networks from a mathematical viewpoint Reasoning under uncertainty Interdisciplinary applications of mathematical theory.